# How do you multiply 8sqrt2 * 8sqrt2?

Sep 13, 2015

128

#### Explanation:

You may simply multiply all the numbers together.
Since multiplication of real numbers is commutative, you may interchange the order to make it easier.

$\therefore 8 \sqrt{2} \cdot 8 \sqrt{2} = 8 \cdot 8 \cdot \sqrt{2} \cdot \sqrt{2}$
$= 64 \cdot 2 = 128$

Another way of looking at it is by using the laws of exponents (indices) and saying that

$8 \sqrt{2} \cdot 8 \sqrt{2} = {\left(8 \sqrt{2}\right)}^{2}$
$= {8}^{2} \cdot {\left(\sqrt{2}\right)}^{2}$
$= 64 \times 2 = 128$