How do you tell if a number is a square number?

Answer 1

two of the same numbers that are times together will equal that number.

example 49

7 x 7 = 49 - no, that's not what the question is asking, everyone should know that. it's like numbers that are like, 349753469576. how would you be able to tell if they're square numbers?

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with larger numbers you have to use a calculator. or start multiplying really big numbers together. - then how would you tell without a calculator?

Answer 2

There is no easy way to find out if a number is a perfect square. The only two way (that I can think of) is to factorise it. If any factor appears twice, then the original number is a perfect square if and only if its quotient, when divided by the twin-factors is a perfect square.

You could try using a calculator to find the square root, but then you need to be very careful about rounding. I just tried sqrt(31381059610) and got 177147.00000. Is that integer enough for you? Actually not, because with one more decimal digit, it is 177147.000003 so 31381059610 is not a square. In fact it is one more than the square of 3^11.

The digital root of 31381059609 is 45 so it is divisible by 3*3 and we can discard that pair of factors. That is, 31381059609 is a perfect square if and only if 31381059609/9 is one. So we need 3486784401 to be a perfect square.

Repeat that process lots of times and you will end up with 1, which is a perfect square.