# How do you simplify 3+sqrt2-7+3sqrt2?

Jan 13, 2017

See the full simplification process below:

#### Explanation:

First, we can group like terms:

$3 + \sqrt{2} - 7 + 3 \sqrt{2} \to 3 - 7 + \sqrt{2} + 3 \sqrt{2}$

We can now group like terms:

$3 - 7 + 1 \sqrt{2} + 3 \sqrt{2} \to - 4 + \left(1 + 3\right) \sqrt{2} \to$

$- 4 + 4 \sqrt{2} \to 4 \left(- 1 + \sqrt{2}\right) \to 4 \left(\sqrt{2} - 1\right)$

We can now take the square root of 2 and calculate the value of the expression:

$4 \left(\sqrt{2} - 1\right) = 4 \left(1.414 - 1\right) = 4 \times 0.414 = 1.656$ to the nearest thousandth.