Square roots & cube roots

###Square roots

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 $\sqrt{ }$ .

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

Example:

$\blueD4 \times \blueD4$ or $\blueD4^2$ $= \greenD{16}$

So $\sqrt{\greenD{16}} = \blueD4$

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

Want to learn more about finding square roots? Check out this video.

##Finding square roots

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

Example:

$\Large{\sqrt{36} = \text{?}}$

Here is the factor tree for $36$:

[[☃ image 1]]

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

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

Notice that we can rearrange the factors like so:

$36 = 2 \times 2 \times 3 \times 3 = \left(2\times 3\right) \times \left(2 \times 3\right)$

So $\left(2\times 3\right)^2 = 6^2 = 36$.

So, $\sqrt{36}$ is $ 6$.

##Practice

[[☃ graded-group-set 1]]

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

Or this challenge exercise:
Equations with square and cube roots

###Cube roots

The cube root of a number is the factor that we multiply by itself three times to get that number.

The symbol for cube root is $\sqrt[3]{}$ .

Finding the cube root of a number is the opposite of cubing a number.

Example:

$\purpleD3\times \purpleD3\times \purpleD3$ = $\purpleD3^\pink3 = \greenD{27}$

So $\sqrt[\pink3]{\greenD{27}}$ = $\purpleD3$

Want to learn more about finding cube roots? Check out this video.

##Finding cube roots

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

Example:

$\Large{\sqrt[3]{64} = \text{?}}$

Here is the factor tree for $64$:

[[☃ image 1]]

So the prime factorization of $64$ is $2\times 2\times 2\times 2\times 2\times 2$.

We're looking for $\sqrt[3]{64}$, so we want to split the prime factors into three identical groups.

Notice that we can rearrange the factors like so:

$64 = 2\times 2\times 2\times 2\times 2\times 2 = \left(2\times 2\right)\times\left(2\times 2\right)\times\left(2\times 2\right)$

So $\left(2\times 2\right)^3 = 4^3 = 64$.

So $\sqrt[3]{64}$ is $4$.

##Practice

[[☃ graded-group-set 1]]

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

Or this challenge exercise:
Equations with square and cube roots