# Multiplying Radical Expressions

In this video, we will multiply radical expressions.

Let’s start with simple expressions.
$\sqrt{3}\times\sqrt{3}=\sqrt{9}=3$
$\sqrt{5}\times\sqrt{5}=\sqrt{25}=3$

In other words,
$\sqrt{7}\times\sqrt{7}=7$
$\sqrt{12}\times\sqrt{12}=12$

Let’s try other examples:
$\sqrt{5}\times\sqrt{7}$ would equal to $\sqrt{35}$
$\sqrt{18}\times\sqrt{2}$ would equal to $\sqrt{36}$, which is a perfect square so it would be $6$

Let’s try the same problem by using another method:
$\sqrt{18}\times\sqrt{2}$ would equal to $\sqrt{36}$ can also be written as $\sqrt{9}\times\sqrt{2}\times\sqrt{2}$
This also leads to the answer of 6

For $\sqrt{15}\times\sqrt{45}$, it would equal to $\sqrt{675}$
25 goes into 675 twenty-seven times
Since 5 is the square root of 25, $\sqrt{675}$ can be written as $5\sqrt{27}$
This can be further simplified into $15\sqrt{3}$