# How do you simplify sqrt 2(sqrt2-sqrt 3)?

Mar 25, 2018

$2 - \sqrt{6}$

#### Explanation:

$\sqrt{2} \left(\sqrt{2} - \sqrt{3}\right)$

Expand,

$\sqrt{2} \cdot \sqrt{2} - \sqrt{2} \cdot \sqrt{3}$

Simplify,

$2 - \sqrt{6}$

Mar 25, 2018

$2 - \sqrt{6}$

#### Explanation:

Did you know that if you had, say $\sqrt{a} \times \sqrt{b}$ it is the same as $\sqrt{a \times b}$

Not in this question but also $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$
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Given: color(blue)(sqrt(2))color(green)((sqrt(2)-sqrt(3))

Multiply everything inside the bracket by the $\textcolor{b l u e}{\sqrt{2}}$ that is outside it.

$\textcolor{g r e e n}{\left[\textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l u e}{\sqrt{2}} \times \sqrt{2} \textcolor{w h i t e}{\frac{2}{2}}\right] - \left[\textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l u e}{\sqrt{2}} \times \sqrt{3} \textcolor{w h i t e}{\frac{2}{2}}\right]}$

color(green)(color(white)("dd")sqrt(2xx2)color(white)("ddddd")-color(white)("d")color(white)("d")sqrt(2xx3)

color(green)(color(white)("dddddddddddd")2-sqrt(6)