How do you rationalize the denominator and simplify $\sqrt[3]{\frac{3 a^{8}}{4 b}}$ $root3((3a^8)/(4b))$ ?

Question

How do you rationalize the denominator and simplify $\sqrt[3]{\frac{3 a^{8}}{4 b}}$ $root3((3a^8)/(4b))$ ?

2 Answers

Impact of this question

1628 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-19T16:25:06

$\frac{\sqrt[3]{6 a^{8} b^{2}}}{2 b}$ $frac(root(3)(6 a^(8) b^(2)))(2 b)$

Explanation:

We have: $\sqrt[3]{\frac{3 a^{8}}{4 b}}$ $root(3)(frac(3 a^(8))(4 b))$

$= \frac{\sqrt[3]{3 a^{8}}}{\sqrt[3]{4 b}}$ $= frac(root(3)(3 a^(8)))(root(3)(4 b))$

$= \frac{\sqrt[3]{3 a^{8}}}{\sqrt[3]{4 b}} \cdot \frac{\sqrt[3]{4 b}}{\sqrt[3]{4 b}} \cdot \frac{\sqrt[3]{4 b}}{\sqrt[3]{4 b}}$ $= frac(root(3)(3 a^(8)))(root(3)(4 b)) cdot frac(root(3)(4 b))(root(3)(4 b)) cdot frac(root(3)(4 b))(root(3)(4 b))$

$= \frac{\sqrt[3]{48 a^{8} b^{2}}}{4 b}$ $= frac(root(3)(48 a^(8) b^(2)))(4 b)$

$= \frac{\sqrt[3]{48} \cdot \sqrt[3]{a^{8}} \cdot \sqrt[3]{b^{2}}}{4 b}$ $= frac(root(3)(48) cdot root(3)(a^(8)) cdot root(3)(b^(2)))(4 b)$

$= \frac{\sqrt[3]{2 \cdot 2 \cdot 2 \cdot 6} \cdot \sqrt[3]{a^{8}} \cdot \sqrt[3]{b^{2}}}{4 b}$ $= frac(root(3)(2 cdot 2 cdot 2 cdot 6) cdot root(3)(a^(8)) cdot root(3)(b^(2)))(4 b)$

$= \frac{\sqrt[3]{2 \cdot 2 \cdot 2} \cdot \sqrt[3]{6} \cdot \sqrt[3]{a^{8}} \cdot \sqrt[3]{b^{2}}}{4 b}$ $= frac(root(3)(2 cdot 2 cdot 2) cdot root(3)(6) cdot root(3)(a^(8)) cdot root(3)(b^(2)))(4 b)$

$= \frac{2 \sqrt[3]{6 a^{8} b^{2}}}{4 b}$ $= frac(2 root(3)(6 a^(8) b^(2)))(4 b)$

$= \frac{\sqrt[3]{6 a^{8} b^{2}}}{2 b}$ $= frac(root(3)(6 a^(8) b^(2)))(2 b)$

Answer 2 · 2017-05-19T16:38:00

$\frac{\sqrt[3]{6 a^{8} b^{2}}}{2 b}$ $color(blue)((root3(6a^8b^2))/(2b)$

Explanation:

$\sqrt[3]{\frac{3 a^{8}}{4 b}}$ $root3((3a^8)/(4b)$

$:.=((3a^8)/(4b))^(1/3)$

$:.=(3^(1/3)a^(8/3))/(4^(1/3)b^(1/3))$

$:.=(root3(3)root3(a^8))/(root3(4)root3(b))$

$:.=root3(3a^8)/(root3(4b))$

$:.=root3(3a^8)/(root3(4b)) xx (root3(4b))/(root3(4b))xx (root3(4b))/(root3(4b))$

$:.=root3(3a^8*4b*4b)/(4b)$

$:.=root3(4b) xx root3(4b) xxroot3(4b) =4b$

$:.=(root3(2*2*2*2*3a^8b^2))/(4b)$

$:.=root3(2) xx root3(2) xx root3(2)=2$

$:.=(cancel2^1root3(6a^8b^2))/(cancel4^2b)$

$:.=color(blue)(root3(6a^8b^2)/(2b)$

Science

Math

Humanities

... and beyond

How do you rationalize the denominator and simplify $\sqrt[3]{\frac{3 a^{8}}{4 b}}$ $root3((3a^8)/(4b))$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you rationalize the denominator and simplify root3((3a^8)/(4b))3√3a84broot3((3a^8)/(4b))?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you rationalize the denominator and simplify $\sqrt[3]{\frac{3 a^{8}}{4 b}}$ $root3((3a^8)/(4b))$ ?