# How do you simplify (3sqrt5)(2sqrt10)?

Aug 6, 2017

$30 \sqrt{2}$

#### Explanation:

When multiplying coefficients (the whole number) with radicands (the numbers under the square root signs), we multiply them with the other of the same kind.

Hence:

$\left(3 \sqrt{5}\right) \left(2 \sqrt{10}\right)$

$\implies \left(3 \times 2\right) \left(\sqrt{5} \times \sqrt{10}\right)$

The radicands are multiplied under one square root sign.

$\implies \left(6\right) \left(\sqrt{5 \times 10}\right)$

$\implies 6 \sqrt{50}$

We can factorise the radicand to simplify it.

$\implies 6 \left(\sqrt{5 \cdot 5 \cdot 2}\right)$

Taking out the $5$ we get:

$\implies 6 \times 5 \sqrt{2}$

$\implies 30 \sqrt{2}$