Someone explain why each nonzero integer has two square roots but only one cube root

The square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. But note that (−4) × (−4) = 16 also, so −4 is also a square root of 16.  This is why each nonzero interger has two square roots.

The cube root of a number is a special value that, when used in a multiplication three times, gives that number. Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3.    But cube root is unlike square root where as -3 × -3 × -3 = -27 not 27 therefore there is only one cube root.

I hope this helps

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