# How do you simplify (2sqrt10)(4sqrt15)?

May 25, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(2 \cdot 4\right) \left(\sqrt{10} \cdot \sqrt{15}\right) \implies 8 \left(\sqrt{10} \cdot \sqrt{15}\right)$

Next, use this rule for exponents to combine the radicals:

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

$8 \left(\sqrt{10} \cdot \sqrt{15}\right) \implies 8 \sqrt{10 \cdot 15} \implies 8 \sqrt{150}$

We can rewrite this as:

$8 \sqrt{25 \cdot 6}$

We can use the above rule for radicals in reverse to simplify the radical term:

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

$8 \left(\sqrt{25 \cdot 6}\right) = 8 \left(\sqrt{25} \cdot \sqrt{6}\right) \implies 8 \left(5 \cdot \sqrt{6}\right) \implies$

$\left(8 \cdot 5\right) \sqrt{6} \implies$

$40 \sqrt{6}$