2 added 11 characters in body; edited body
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Seriously, 1112 bytes

,iZ`i-ª`MΣ√ª`MΣ√A

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Explanation:

,iZ`i-ª`MΣ√ª`MΣ√A
,iZ           get input, flatten, zip
   `   `M     map:
    i-ª         flatten, subtract, square
         Σ√Σ√A  sum, sqrt, abs

Seriously, 11 bytes

,iZ`i-ª`MΣ√

Try it online!

Explanation:

,iZ`i-ª`MΣ√
,iZ          get input, flatten, zip
   `   `M    map:
    i-ª        flatten, subtract, square
         Σ√  sum, sqrt

Seriously, 12 bytes

,iZ`i-ª`MΣ√A

Try it online!

Explanation:

,iZ`i-ª`MΣ√A
,iZ           get input, flatten, zip
   `   `M     map:
    i-ª         flatten, subtract, square
         Σ√A  sum, sqrt, abs
1
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Seriously, 11 bytes

,iZ`i-ª`MΣ√

Try it online!

Explanation:

,iZ`i-ª`MΣ√
,iZ          get input, flatten, zip
   `   `M    map:
    i-ª        flatten, subtract, square
         Σ√  sum, sqrt