How to Find a Square Root
Question
To find the square root of 72, the first thing you want to do is factor 72 into its
00:00
00:00
Hi, my name is Bassem Saad. I'm an associate math instructor and a Ph.D. candidate, and I'm here today for About.com to show you how to find the square root of a positive integer.
Instructions for How to Find a Square Root

So say you want to find the square root of 72. Well, the first thing you want to do is factor 72 into its primes. So, 72 factors into two, times two, times two, times three, times three. The second step is to pair repeated primes. So you have two, times two grouped together; you have an odd two, so you leave it alone; then you have a three, times three grouped together. In the third step, you want to factor out pairs of primes.

So what happens is that when you have this pair: two, times two – when you pull it past the square root symbol, you lose one of the two's. And so, this two, times two becomes just two. And likewise, this three, times three becomes three. So the square root of 72 can be simplified down to six, times the square root of two. So let's take a look at another example: the square root of 625.
Example of How to Find a Square Root

So again, our first step is to factor 625 into its primes. So that's five, times five, times five, times five. Then you want to group pairs of repeated primes, so the first pair is five, times five. We have another pair of five, times five. In the last step, we want to factor out the grouped pairs of repeated primes. So you want to factor out five, times five from the square root. Well, that's the same thing as saying five squared – five, times five is five squared – and the square root is the inverse operation of five squared. So, the square root of five squared is five. And we have two five, times fives, so we're going to factor out and get five. We'll factor out the other pair and get another five. So our solution is five, times five, or 25. So now you know how to find square roots.