Hey there! I'm happy to help!
A perfect square is a number whose prime factors can be multiplied together to obtain two identical factors.
Look at 64. It's prime factors are 2×2×2×2×2×2. If we multiply these 2's together to obtain two identical numbers, then 64 is a perfect square.
We see that there are six twos being multiplied. So, that means we have two groups of three twos, and since they both have three twos, they are identical! Three twos multiplied is 8, and 8²=64. Pretty cool right?
Now, we need to find identical groups of these numbers. We have two sevens, two 2's and one three. We could have two groups with one 7 and one 2, but this extra 5 would throw it off balance, so we cannot obtain two equal numbers from this.
Therefore, this number is not a perfect square.
I hope that this helps! Have a wonderful day!
