# How do you simplify 4sqrt2*5sqrt8?

Apr 20, 2017

See the entire solution process below:

#### Explanation:

The rule for multiplying radicals is:

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

Using this rule, rewrite this expression as:

$\left(4 \cdot 5\right) \left(\sqrt{2} \cdot \sqrt{8}\right) \implies 20 \sqrt{2 \cdot 8} = 20 \sqrt{16}$

Now, take the square root of 16 remembering the square root of a number produces a negative and positive result:

Solution 1)

$20 \sqrt{16} \implies 20 \cdot - 4 \implies - 80$

Solution 2)

$20 \sqrt{16} \implies 20 \cdot 4 \implies 80$

The solution is $\pm 80$