# How do you simplify (sqrt2) + 2 (sqrt2) + (sqrt8) / (sqrt3)?

Jul 12, 2018

$\frac{\sqrt{2}}{3} \left(9 + 2 \sqrt{3}\right)$

#### Explanation:

$\sqrt{2} + 2 \cdot \sqrt{2} + 2 \frac{\sqrt{2}}{\sqrt{3}}$
since $\sqrt{8} = 2 \sqrt{2}$

(sqrt(2)`sqrt(3)+2*sqrt(2)*sqrt(3)+2sqrt(2))/sqrt(3)

multiplying numerator and denominator by $\sqrt{3}$

$\frac{\sqrt{2}}{3} \left(3 + 2 \cdot 3 + 2 \cdot \sqrt{3}\right)$

and this is

$\frac{\sqrt{2}}{3} \left(9 + 2 \cdot \sqrt{3}\right)$

Jul 12, 2018

sqrt2+2sqrt2+(sqrt8)/(sqrt3)=color(blue)(3sqrt2+(2sqrt6)/3

#### Explanation:

Simplify:

$\sqrt{2} + 2 \sqrt{2} + \frac{\sqrt{8}}{\sqrt{3}}$

Simplify $\sqrt{8}$.

$\sqrt{2} + 2 \sqrt{2} + \frac{\sqrt{2 \times 2 \times 2}}{\sqrt{3}}$

$\sqrt{2} + 2 \sqrt{2} + \frac{\sqrt{{2}^{2} \times 2}}{\sqrt{3}}$

Apply square root rule: $\sqrt{{a}^{2}} = a$

$\sqrt{2} + 2 \sqrt{2} + \frac{2 \sqrt{2}}{\sqrt{3}}$

Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{3}$.

$\sqrt{2} + 2 \sqrt{2} + \frac{2 \sqrt{2} \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Apply square root rule: $\sqrt{a} \sqrt{a} = a$

$\sqrt{2} + 2 \sqrt{2} + \frac{2 \sqrt{2} \sqrt{3}}{3}$

Apply square root rule: $\sqrt{a} \sqrt{b} = \sqrt{a b}$

$\sqrt{2} + 2 \sqrt{2} + \frac{2 \sqrt{6}}{3}$

Simplify.

$3 \sqrt{2} + \frac{2 \sqrt{6}}{3}$