# How do you simplify sqrt392?

Aug 18, 2016

$14 \sqrt{2}$

#### Explanation:

When simplifying roots of Natural numbers it is often useful to express the number as the product of prime numbers.

Note: $392 = 2 \times 2 \times 2 \times 7 \times 7$

Therefore: $\sqrt{392} = \sqrt{2 \times 2 \times 2 \times 7 \times 7}$

For every pair of prime factors can then be taken through the sqrt as follows:

$\sqrt{392} = 2 \times 7 \times \sqrt{2}$

$\sqrt{392} = 14 \sqrt{2}$