# How do you simplify sqrt 90 times sqrt 40 - sqrt 8 times sqrt 18?

Apr 22, 2017

$\textcolor{b l u e}{48}$

#### Explanation:

$\sqrt{90} \times \sqrt{40} - \sqrt{8} \times \sqrt{18}$

$\therefore = \sqrt{3 \cdot 3 \cdot 10} \times \sqrt{2 \cdot 2 \cdot 10} - \sqrt{2 \cdot 2 \cdot 2} \times \sqrt{3 \cdot 3 \cdot 2}$

$\therefore \sqrt{3} \cdot \sqrt{3} = 3 , \sqrt{2} \cdot \sqrt{2} = 2$

$\therefore = 3 \sqrt{10} \times 2 \sqrt{10} - 2 \sqrt{2} \times 3 \sqrt{2}$

$\therefore = 6 \times 10 - 6 \times 2$

:.color(blue)(60-12=48

Apr 22, 2017

$60 - 12 = 48$

#### Explanation:

If you are multiplying the same roots you can combine them into one root:

Here we are multiplying square roots:

$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$

$\sqrt{90} \times \sqrt{40} - \sqrt{8} \times \sqrt{18}$

In this case they multiply to give perfect squares:

$= \sqrt{3600} - \sqrt{144} \text{ } \leftarrow$ find the roots

$= 60 - 12$

$= 48$