# How do you simplify root3(4x^2)color(white)(..)root3(8x^7)?

##### 2 Answers
Apr 12, 2018

${2}^{\frac{5}{3}} {x}^{3}$

#### Explanation:

$\sqrt{x}$ = ${x}^{\frac{1}{2}}$

So we can change the question to

${\left(4 {x}^{2}\right)}^{\frac{1}{3}}$$\times$${\left(8 {x}^{7}\right)}^{\frac{1}{3}}$

${4}^{\frac{1}{3}} {x}^{\frac{2}{3}}$$\times$${8}^{\frac{1}{3}} {x}^{\frac{7}{3}}$

$4 = {2}^{2}$ so ${4}^{\frac{1}{3}}$=${\left({2}^{2}\right)}^{\frac{1}{3}}$=${2}^{\frac{2}{3}}$

${8}^{\frac{1}{3}} = 2$

So the question becomes

${2}^{\frac{2}{3}} {x}^{\frac{2}{3}}$$\times$$2 {x}^{\frac{7}{3}}$ = ${2}^{\frac{5}{3}} {x}^{\frac{9}{3}}$ = ${2}^{\frac{5}{3}} {x}^{3}$

Apr 12, 2018

${2}^{\frac{5}{3}} {x}^{3}$

#### Explanation:

Expression $= \sqrt{4 {x}^{2}} \sqrt{8 {x}^{7}}$

Remember: $\sqrt{a} \times \sqrt{b} = \sqrt{a b}$

Hence, Expression $= \sqrt{4 {x}^{2} \times 8 {x}^{7}}$

$= \sqrt{32 {x}^{9}}$

$= \sqrt{32} \times \sqrt{{x}^{9}}$

$= \sqrt{{2}^{5}} \times \sqrt{{x}^{9}}$

$= {2}^{\frac{5}{3}} \times {\left({x}^{9}\right)}^{\frac{1}{3}}$

$= {2}^{\frac{5}{3}} {x}^{3}$