JavaScript (ES6), 13 bytes
n=>!(n**.5%1)
Returns true if the square root of n is a whole number.
Snippet:
f=
n=>!(n**.5%1)
console.log(f(0));
console.log(f(1));
console.log(f(2));
console.log(f(4));
console.log(f(8));
console.log(f(16));
console.log(f(88));
console.log(f(2147483647));
Rick Hitchcock
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