# How do you simplify 4sqrt8*sqrt2?

Sep 7, 2017

1) $4 \sqrt{4 \times 2} \cdot \sqrt{2}$

2) (4sqrt4*sqrt2) ⋅ $\sqrt{2}$

3) $4 \times 2 \sqrt{2} \cdot \sqrt{2}$

4) $8 \cdot 2$

5) $16$

#### Explanation:

1) Find factors of $8$ under the radical.
2) Simplify $\sqrt{4}$ to $2$ and multiply by the $4$ outside
3) Multiply 8sqrt2*sqrt2" "(larrsqrt2*sqrt2 equals 2)
4) $8 \cdot 2$
5) $16$

Sep 7, 2017

$= 16$

#### Explanation:

The two square roots can be combined into one. In this case this is a good idea because the product will be a prefect square.

$4 \sqrt{8} \times \sqrt{2} = 4 \sqrt{8 \times 2}$

$= 4 \sqrt{16}$

$= 4 \times 4$

$= 16$