# How do you simplify 9sqrt 8 - sqrt72 + sqrt98?

Sep 8, 2016

$19 \sqrt{2}$

#### Explanation:

Write the numbers under the roots as the product of their prime factors.

$9 \sqrt{8} - \sqrt{72} + \sqrt{98}$

=$9 \sqrt{2 \times 2 \times 2} - \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{7 \times 7 \times 2}$

Find the square roots where possible

=$9 \times 2 \sqrt{2} - 2 \times 3 \sqrt{2} + 7 \sqrt{2} \text{ } \leftarrow$ there is a common factor

=$\sqrt{2} \left(18 - 6 + 7\right)$

=$19 \sqrt{2}$