What is the square root of 3-2sqrt2?

Jan 18, 2017

$\sqrt{3 - 2 \sqrt{2}} = \sqrt{2} - 1$

Explanation:

$3 - 2 \sqrt{2}$

= $2 - 2 \sqrt{2} + 1$

= ${\left(\sqrt{2}\right)}^{2} - 2 \times \sqrt{2} \times 1 + {1}^{2}$

= ${\left(\sqrt{2} - 1\right)}^{2}$

Hence $\sqrt{3 - 2 \sqrt{2}} = \sqrt{2} - 1$