Riya says the square root of 64 is 32, because a square root means halving — undoing a doubling

Why

Riya has mixed up two different operations that both sound like making a number smaller. Squaring a number is not doubling it, so a square root is not halving it. Squaring means multiplying a number by ITSELF: 8 squared is 8 times 8, which is 64. So the square root of 64 asks 'what number times itself gives 64?', and the answer is 8. Halving 64 gives 32, but 32 times 32 is 1024, nowhere near 64. Test: try a number where doubling and squaring happen to match, like 2, whose double is 4 and whose square is also 4 — that coincidence is what makes the mix-up feel right; now try 3, where the double is 6 but the square is 9, and the two clearly part ways. Aman is right, the square root of 64 is 8: a square root undoes multiplying a number by itself, not doubling it.