# How do you simplify sqrt3*sqrt6?

May 29, 2017

$3 \sqrt{2}$

#### Explanation:

$\text{using the "color(blue)"laws of radicals}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}} \sqrt{a} \times \sqrt{b} \Leftrightarrow \sqrt{a b}$

$\Rightarrow \sqrt{3} \times \sqrt{6} = \sqrt{3 \times 6} = \sqrt{18}$

$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \times \sqrt{2}$

$\Rightarrow \sqrt{3} \times \sqrt{6} = 3 \sqrt{2}$

May 29, 2017

$= 3 \sqrt{2}$

#### Explanation:

Remember that if you multiplying or dividing square roots, you can combine them into one.

$\sqrt{3} \times \sqrt{6} = \sqrt{3 \times 6} \text{ } \leftarrow$ factor $6$

$= \sqrt{3 \times 3 \times 2} = \sqrt{{3}^{2} \times 2}$

Now find the roots where possible:

$= 3 \sqrt{2}$

May 29, 2017

color(blue)(=3sqrt2

#### Explanation:

$\sqrt{3} \cdot \sqrt{6}$

$\therefore = \sqrt{6 \cdot 3}$

$\therefore = \sqrt{2 \cdot \underline{3 \cdot 3}}$

$\therefore = \sqrt{3} \times \sqrt{3} = 3$

:.color(blue)(=3sqrt2

check:

:.color(blue)(sqrt3 xx sqrt6=4.242640687

:.color(blue)(3 xx sqrt2 =4.242640687