# root of root of root of root

This idea came to me when I saw my little brother playing with my calculator :D

Taking a integer as an input, print that many graphical square roots under each other, like this:

n = 1

___
\/ 1

n = 3
_______
/ _____
/ / ___
\/\/\/ 3

n = 5

___________
/ _________
/ / _______
/ / / _____
/ / / / ___
\/\/\/\/\/ 5

n = 10

______________________
/ ____________________
/ / __________________
/ / / ________________
/ / / / ______________
/ / / / / ____________
/ / / / / / __________
/ / / / / / / ________
/ / / / / / / / ______
/ / / / / / / / / ____
\/\/\/\/\/\/\/\/\/\/ 10


Each root consists of 4 parts, which I'm going to very scientifically name:

(s is the root size on the stack of roots, n is the input number, x is the number of digits)

1. The "tail", which is a single \
2. The "wall", which consists of / * s
3. The "roof", which consists of _ * 2 * s + x
4. And the number n under the smallest root, placed in the centre (leaving one empty space under the last _ in the smallest root)

# Input

You must take input of the number n, no hardcoding the n

# Output

This is a code-golf challenge, so lowest byte count for each language wins!

• Will the number exceed the digit 9?
– user92069
Commented May 9, 2020 at 8:36
• @Λ̸̸ good catch, will edit the rules. Yes, it can exceed the digit 9, updating the rules to clarify what to do
– Dion
Commented May 9, 2020 at 8:38
• Related (the same idea, but different art) Commented May 9, 2020 at 12:10
• Why does the input have to be from STDIN and out to STDOUT? That seems like an unnecessarily arbitrary restriction. Commented May 9, 2020 at 14:12
• @RossPresser Less interesting than you might think: with input s as a string, l = s.splitlines()[-1]; print(int(l[l.index(' '):]) ** (1 / l.count('/'))). Commented May 11, 2020 at 18:31

# Python 2, 104948981 79 bytes

s=n=input()
while s:print' '*s,'/ '*(n-s)+'_'*(2*s+len(n));s-=1
print'\/'*n,n


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Edit 1: Forgot I switched to python 2 lol

Edit 2: Thanks @ElPedro for the idea of switching to while loop!

Edit 3: Thanks @SurculoseSputum for saving 8 bytes!

Edit 4: Thanks @xnor for saving 2 bytes!

• @Λ̸̸ XD my answer could probably be much shorter
– Dion
Commented May 9, 2020 at 9:03
• You posted a minute before I did and mine is so similar that I'll delete and try to golf yours instead :) Commented May 9, 2020 at 9:09
• @ElPedro yep, I saw your answer and remembered that i switched to python 2 for all of the savings)
– Dion
Commented May 9, 2020 at 9:10
• @ElPedro 89 bytes :)
– Dion
Commented May 9, 2020 at 9:18
• @Dion -~ bitwise negates (evaluated -1-x), then negates. This basically increments the number. You can take a look at this post.
– user92069
Commented May 9, 2020 at 9:47

# JavaScript (ES6),  104 102  99 bytes

A recursive function starting with the last line and using regular expressions to update each line above.

f=(n,s='\\/'.repeat(n)+(e=' ')+n)=>~n?f(n-1,e+s.replace(/\\/g,e).replace(/.(?!.*\/)/g,'_'))+
+s:e


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## How?

### Initialization

We generate the bottom line with:

s = '\\/'.repeat(n) + (e = ' ') + n


For instance, this gives "\/\/\/\/ 4" for $$\n=4\$$.

### Recursion

We get rid of the backslashes with:

s.replace(/\\/g, e)


We create the 'roof' or increase its size with:

.replace(/.(?!.*\/)/g, '_')


which means: replace with an underscore each character that doesn't have any slash on its right.

 _________
/ _______
/ / _____
/ / / ___
\/\/\/\/ 4


And with a leading space inserted at each iteration:

     _________
/ _______
/ / _____
/ / / ___
\/\/\/\/ 4


# Erlang (escript), 188 bytes

f(0,N)->string:copies("\\/",N)++" "++integer_to_list(N);f(X,N)->string:copies(" ",X+1)++string:copies("/ ",N-X)++string:copies("_",2*X+floor(math:log10(N)+1))++"
"++f(X-1,N).
f(N)->f(N,N).


Try it online!

# Explanation

f(N)->f(N,N).   % Assign the counter to the input.
f(X,N)->        % While the counter isn't 0:
string:copies(" ",X+1)
%     Repeat the space counter + 1 times

++string:copies("/ ",N-X)
%     Repeat "/ " input - counter times

++string:copies("_",
%     Repeat the "_" that many times:

2*X             %     The counter doubled
+floor(math:log10(N)+1)
%     Plus the length of the digit(s) of the input
++"
"               %     Join the above, and append a newline
++f(X-1,N).     %     Decrement the counter by 1

f(0,N)->        % If the counter turns into 0:
string:copies("\\/",N)
%     Repeat "\/" input times

++" "           %     Append a space
++integer_to_list(N);
%     Append the number converted into a string
$$$$


# Mathematica (Notebook) 30 bytes

Only in Spirit ;-)

Nest[Defer@√#&,#,#]&@Input[]


in the spirit but not the letter of the problem.

# Explanation

Input[]              //take input

Nest[f,expr,n]       //apply f to expr n times i.e. f[f[f[f[f....[expr]]..]] with n fs
Nest[f,#,#]&         //define a lambda that applies f to arg #, # times
Nest[f,#,#]&@Input[] //apply the lambda Nest[f,#,#]& to the value of Input[]

√#&                  //define a lambda that puts arg # inside √
Defer@√#&            //define a lambda that puts arg # inside √ buts keeps the mathematical square root unevaluated

Nest[Defer@√#&,#,#]&@Input[]
//apply the lambda Defer@√#& to Input, Input no of times



# 05AB1E, 30 bytes

-4 bytes thanks to Kevin Cruijssen.

Lε-„/ ×'_y·¹g+×«y>ú}R„\/¹×¹‚ª»


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• ð«¹« can be ¹‚ for -2 (» will join all inner lists by spaces before joining by newlines). And another -2 by changing >ð×„/ ¹y-×'_y·¹g+×J to -„/ ×'_y·¹g+×«y>ú (the ¹y- has been golfed to - for -2, and the >ð× has been replaced with a trailing y>ú for the same byte-count). So combined it's 30 bytes. Commented May 11, 2020 at 6:31
• 29 bytes Commented Mar 3, 2022 at 9:38

# Pyth, 34 bytes

VQj*N"/ ",*hJ-QNd*+lQyJ\_;jd,*"\/


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VQ


Loop the variable N over 0 to Q (the input) minus 1

j*N"/ "


Join the following using N instances of "/ ":

,


The two element list of...

*hJ-QNd


... {Q - N + 1} space characters (d is the space character in Pyth). Store the value of Q minus N in the variable J so we can use it later.

*+lQyJ\_


... {J times 2, plus the number of digits of Q} instances of the string "_"

;


End of loop

jd,*"\/


Join the following using a space:

• Q instances of the string "\/"

• Q casted to a string

Conveniently, the string literal is implicitly closed, and the two Qs are implicitly appended to the end of the program.

# PowerShell, 88 84 bytes

param($n)1..$n|%{' '*($m=$n- --$_)+' /'*$_+' '+'_'*(2*$m+"$n".length)}
'\/'*$n+"$n"


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# Charcoal, 30 bytes

ＮηＧ↙η←⁺²Ｌθ↖η_Ｍη↘Ｐθ←←Ｆη«Ｐ↗⊕ι←/\


Try it online! Link is to verbose version of code. Explanation:

Ｎη


Input n as a number.

Ｇ↙η←⁺²Ｌθ↖η_


Print the "roof", ensuring that it is long enough to overhang n.

Ｍη↘Ｐθ←←


Print n as a string in the appropriate place.

Ｆη«


Loop n times.

Ｐ↗⊕ι


Print the next diagonal line of the "wall".

←/\


Print the next part of the "tail".

# MATL, 43 bytes

:P"@QZ"47Oh1X@qX"95GVn@E+Y"hh]'\/'1GX"0GVhh


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First time I have used X", Y", Z" in the same answer!

# Jelly, 36 bytes

DLṭ1j+1,-,2×Ɱ$“ “/ “_”ẋ"ⱮṚṄ€ȧ⁾\/ẋ,⁸K  A full program which prints the result. Try it online! ### How? DLṭ1j+1,-,2×Ɱ$“ “/ “_”ẋ"ⱮṚṄ€ȧ⁾\/ẋ,⁸K - Main Link: integer, n
D                                    - digits (n)
L                                   - length
ṭ1                                 - tack to one
j                                - join with (n)
$- last two links as a monad - f(n): 1,-,2 - [1,-1,2] Ɱ - map across [1..n] with: × - multiplication + - add (left to each of right, vectorised) “ “/ “_” - [' ', '/ ', '_'] Ɱ - map across (the list of list of numbers) with: " - zipped: ẋ - repetition Ṛ - reverse Ṅ€ - print each with trailing newlines ȧ - logical AND (with n) -> n ⁾\/ - ['\', '/'] ẋ - repeat (n times) ,⁸ - pair with n K - join with a space - implicit print  # MathGolf, 32 bytes {kî-⌠ *_£(∞k£+'_*û/ ï*\n}û\/k* k  Try it online. Explanation: { # Loop the (implicit) input amount of times: k # Push the input-integer î- # Subtract the 1-based loop-index ⌠ # + 2 * # And repeat that many spaces _ # Duplicate this string £ # Pop and push its length ( # + 1 ∞ # * 2 k # Push the input-integer again £ # Pop and push its length + # Add those two integers together '_* '# And repeat that many "_" û/ # Push the 2-char string "/ " ï* # And repeat it the 0-based loop-index amount of times \ # Then swap the top two strings on the stack n # And push a newline character }û\/k* # After the loop: repeat 2-char string "\/" the input amount of times # Push a space k # And push the input-integer # (after which the stack is joined together and output implicitly)  # Wolfram Mathematica 120 bytes a=StringRepeat;b=Print;Input[]; b[a[" ",#+1],a["/ ",%-#],a["_",2#+IntegerLength[%]]]&/@Range[%,1,-1];b[a["\/",%]," ",%];  # Explanation StringRepeat[str,n] //creates a string with str repeated n times a=StringRepeat //alias for StringRepeat Print[expr1,expr2,...] //prints expr1, expr2,... on a newline without separation b=Print //alias for Print Input[] //gets user input, ; //Hide implicit output % //last output IntegerLength[n] //no of digits in n in base 10 a[" ",#+1] //Make a lamba StringRepeat with arg #, that prints " ",#+1 times b[a[" ",#+1],a["/ ",%-#],a["_",2#+IntegerLength[%]]]& //Make a lambda with arg # that //prints the appropriate " /_________" //depending on # b[....]&/@Range[%,1,-1]; //map the lambda b[....] over {%,%-1,%-2,...,1} b[a["\/",%]," ",%]; //print the last row "\/\/\/...\/ "  Link to notebook # C# (Visual C# Interactive Compiler), 217 154 bytes n=>Join("",Range(0,n).Select(i=>new S(' ',n-i+1)+new S('/',i*2)+new S('_',(n-i)*2-~(n+"").Length)+'\n').Concat(Repeat("\\/",n))).Replace("//", "/ ")+" "+n  Try it online! Edit: Removed 19 bytes thanks to @KevinCruijssen, and used the header better(?) • Hi, welcome to CGCC! Unless you use it as a recursive function, you don't need to count the Func<int,string>f= and trailing ; in your byte-count. You can move those to your head & footer of your TIO-link. :) Also, (n+i-n)*2 is basically i*2. And n/10 is incorrect I'm afraid for $n\geq100$. This should be (n+"").Length() instead. In that case, you can also golf the (n-i)*2+1+(n+"").Length() to (n-i)*2-~(n+"").Length() (relevant tip). In total, it'll become 198 bytes. Enjoy your stay! :) Commented May 11, 2020 at 9:36 • @KevinCruijssen Thanks for the comment! And the tips. I saw others but their printing code in the footer, but I didn't know how much, or what, was okay to put in the header/footer. I added your suggestions, and some usings to my answer, do you think it's still acceptable? Commented May 11, 2020 at 15:30 # Haskell, 129 bytes x%s=[1..x]>>s 0#b=b%"\\/"++' ':show b x#b=(x+1)%" "++(b-x)%"/ "++(show b>>"_")++x%"__"++'\n':(x-1)#b f x=x#x main=interact$f.read


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Ties the existing 129 byte answer but is compliant with the challenge by performing full IO.

# Retina 0.8.2, 77 bytes

^
$.'$*_=$'$*/¶$'$*V
/
=$.%'$*=¶  $.%'$* $ = __ (_+)(/+)$2$1 / / V \/ 1A  Try it online! Explanation: ^$.'$*_=$'$*/¶$'$*V  Insert some working elements: enough _s to cover the input, a / for each input, then on the next line, a V for each input (representing \/) and a space. / =$.%'$*=¶$.%'$*$


Now expand the /s into a bottom right triangle, and also add extra _s to overhang on both sides on each line.

=
__


Expand the =s which were placeholders for two _s.

(_+)(/+)
$2$1


Move the input cover next to the rest of the overhang.

/
/


Space the /s apart.

V
\/


Expand the Vs on the last line.

1A


Delete some left-overs.

r=replicate
c=(concat.).r
f n|s<-show n=unlines$map(\o->r(n-o+1)' '++c o"/ "++r(2*(n-o)+length s)'_')[0..n-1]++[c n"\\/"++" "++s]  Try it online! • This challenge has a restricted IO scheme, which does not permit functions. In order for this to be a valid answer you are expected to write a main declaration. Commented May 11, 2020 at 23:27 # Java 11, 137 124 bytes n->{String l="\\/".repeat(n)+" "+n,r=l;for(;n-->0;r=l+"\n"+r)l=" "+l.replace('\\',' ').replaceAll(".(?!.*/)","_");return r;}  -13 bytes by porting @Arnauld's JavaScript answer, so make sure to upvote him! Try it online. Explanation: n->{ // Method with integer parameter and String return-type String l= // Temp-String l for the current line, starting at: "\\/".repeat(n) // The input amount of "\/" +" "+n, // appended with a space and the input r=l; // Result-String, starting at this (last) line for(;n-->0 // Loop n amount of times: ; // After every iteration: r=l+"\n"+r) // Prepend the new l with newline to the result-String l= // Change l to the new line: " " // A space +l // appended with the current line, with the replacements: .replace('\\',' ') // All '\' replaced with spaces .replaceAll(".(?!.*/)","_"); // And all characters NOT followed by a '/' with a "_" return r;} // And return the result-String after the loop  # Julia, 107 bytes n=parse(Int,readline()) println.([[" "^(s+1)*"/ "^(n-s)*"_"^(2s+length("$n")) for s=n:-1:1];"\\/"^n*" $n"])  Try it online! ## Breakdown n = parse(Int, readline()) println.([ # broadcasting with . applies println to each element of vector [ " "^(s + 1)*"/ "^(n - s)*"_"^(2s + length("$n"))
for s ∈ n:-1:1 # array comprehension
];   # semicolon enables blockmatrix-style array syntax...
# ...which unpacks elements in array above into elements of vector
"\\/"^n*" $n" # last element of vector ])  # Python 3, 100, 99 bytes n=int(input()) for i in range(n):print(" "*(n+~i)," /"*i,"_"*(2*n-2*i+len(str(n)))) print("\/"*n,n)  Try it online! thnx to @KevinCruijssen for -1 • n-1-i can be n+~i for -1 (relevant tip). Commented May 11, 2020 at 10:55 # Perl 5-ap, 86 bytes $\=$/.'\\/'x$_." $_";$_=$"x($_+1).'_'x(2*$_+y///c);for$a(1.."@F"-1){say;s, /| __,/ ,g}


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• Nice answer, pretty short too considering the length of a lot of the other answers, you can save a little bit more with some re-ordering and a couple of other tweaks though!: Try it online! Commented Jul 26, 2020 at 11:32

# CJam, 46 bytes

li:A:B;{A)S*"/ "BA-*'_2A*Bs,+*NA(:A}g"\\/"B*SB


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Explanation:

li            take input as integer
:A:B;         assign that to the variables A and B
{             start of while A loop
A)S*          push A-1 spaces
"/ "BA-*      push B-A strings of "/ "
'_2A*Bs,+*    push 2A + the number of digits _
N             push a newline
A(:A          decrement A
}g            end of while loop
"\\/"B*       push B \/
SB            push B after a space


x%y=[1..x]>>y
f x|n<-read x=unlines[(n+1-i)%" "++i%"/ "++(n-i)%"__"++(x>>"_")|i<-[0..n-1]]++n%"\\/"++' ':x
main=interact f


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I've deliberately constrained myself to standard I/O. See my comments on the question.

# VyxalSo, 30 bytes

ɾṘ›?ʀṪ‛/ *꘍?ɾd?L+\_*Ṙ+⁋,‛\/*$"  Try it Online! This code's sorta backwards to reduce stack operations.  ?ɾd # (1...input) * 2 ?L+ # + log_10(input) \_* # That many underscores for each Ṙ+ # Reverse that, and append to... ɾṘ› # (2...input+1) reversed ꘍ # For each, that many spaces appended to each of... ?ʀṪ # 0...input-2 ‛/ * # For each, that many copies of "/ " ⁋, # Print that, joined on newlines ‛\/* # Input * "\/"$" # Paired with input
# (So flags) print that joined by a space


# Perl 5, 96 bytes

sub f{$n=pop;join"\n",(map' 'x($x=1+$n-$_).'/ 'x$_.'_'x($x*2-2+length$n),0..$n-1),'\/'x$n."$n"}


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# PHP, 121 bytes

for($x=($i=$j=$argn)/10+1,$f=str_repeat;$i;$c.="/ ")printf("%{$i}s $c%s\n"," ",$f("_",2*$i--+$x));echo$f("\\/",$j)." \$j";


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This is not that great maybe, but I came with this.

# Pyth, 54 44 bytes

VQ+d++*-QNd*"/ "N*+*2-QNl+""Q"_";++*"\/"hNdQ


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edit 1: Thanks @mathjunkie for saving 10 bytes!

• A few tips: FNrZ can be replaced by V. Each of the space literals (" ") can be replaced by d. Anywhere that you use +1 you can use h instead Commented May 19, 2020 at 14:42

# Pip, 38 bytes

Fi,aP[sYsXa-i"/ "Xi'_Ma.y.y]"\/"Xa.s.a


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### Explanation

This is one of those very rare occasions in Pip when a for loop seems to be the shortest solution.

Fi,aP[sYsXa-i"/ "Xi'_Ma.y.y]"\/"Xa.s.a
s is space; a is 1st command-line arg (implicit)
Fi,a                                    For i in range(a):
P                                    Print, with a newline
[                     ]             the contents of this list, implicitly concatenated:
s                                   A space
sXa-i                             Space, repeated (a-i) times
Y                                   also, yank that string into the y variable
"/ "Xi                       "/ ", repeated (i) times
a.y.y               Concatenate a with y twice
'_M                     and replace each character with an underscore,
giving a string of len(a) + 2 * (a-i) underscores
"\/"Xa      "\/", repeated (a) times
.s    concatenated to space
.a  concatenated to a
Autoprint (implicit)


# MAWP, 138 bytes

%@![1A~!~]%![!!!1M[84W;1A]%\A[95W2M;84W;1A]%2W1M3A{3M[29W1M5W;1A]25W;%1A}]~!!0/[25WP~1M~]%\1A3M[29W1M5W;1A]25W;%[99W25WM1M;95W2M;1A]%84W;:


Works as expected for single digit numbers, but beyond that, the last root will be longer than the others.

Try it!

# Scala, 91 bytes

n=>print(n.to(1,-1).map{i=>" "*(i+1)+"/ "*(n-i)+"_"*(2*i+1)}:+("\\/"*n+" "+n)mkString "\n")


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# Husk, 46 bytes

:§+*"¦/"o:' s¹z+mR' ṫ¹m§+*" /"(:' R'_+L¹D≠¹)ŀ


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