JavaScript on NodeJS & Chrome, 51 bytes

// OLD: t=n=>{i=Number.isSafeInteger;return i(n)&&i(n**.5)}
i=Number.isSafeInteger;t=n=>i(n)&&i(n**.5) 
// TestCases:
let l=console.log;l(`t(1): ${t(1)}; t(64): ${t(64)}; t(88): ${t(88)};`)

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