Square roots review

The square root of a number is the factor that we can multiply by itself to get that number.

The symbol for square root is $\sqrt{ }$square root of, end square root .

Finding the square root of a number is the opposite of squaring a number.

$\blueD4 \times \blueD4$start color #11accd, 4, end color #11accd, times, start color #11accd, 4, end color #11accd or $\blueD4^2$start color #11accd, 4, end color #11accd, squared $= \greenD{16}$equals, start color #1fab54, 16, end color #1fab54

Έτσι $\sqrt{\greenD{16}} = \blueD4$square root of, start color #1fab54, 16, end color #1fab54, end square root, equals, start color #11accd, 4, end color #11accd

If the square root is a whole number, it is called a perfect square! In this example, $\greenD{16}$start color #1fab54, 16, end color #1fab54 is a perfect square because its square root is a whole number.

If we can't figure out what factor multiplied by itself will result in the given number, we can make a factor tree.

Here is the factor tree for $36$36:

So the prime factorization of $36$36 is $2\times 2\times 3\times 3$2, times, 2, times, 3, times, 3.

We're looking for $\sqrt{36}$square root of, 36, end square root, so we want to split the prime factors into two identical groups.

Notice that we can rearrange the factors like so:

So $\left(2\times 3\right)^2 = 6^2 = 36$left parenthesis, 2, times, 3, right parenthesis, squared, equals, 6, squared, equals, 36.

So, $\sqrt{36}$square root of, 36, end square root is $6$6.

Want to try more problems like this? Check out this exercise: Finding square roots

Or this challenge exercise: Equations with square and cube roots