# How do you simplify 7sqrt2 - sqrt32 + sqrt128?

Jul 3, 2016

$11 \sqrt{2}$

#### Explanation:

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

$7 \sqrt{2} - \sqrt{{2}^{5}} + \sqrt{{2}^{7}}$

Make even indices wherever possible, to be able to find the square roots

$7 \sqrt{2} - \sqrt{2 \times {2}^{4}} + \sqrt{2 \times {2}^{6}}$

=$7 \sqrt{2} - {2}^{2} \sqrt{2} + {2}^{3} \sqrt{2} \text{ = } 7 \sqrt{2} - 4 \sqrt{2} + 8 \sqrt{2}$

Now add the like terms: $11 \sqrt{2}$