How do you simplify $\frac{\sqrt{108 x^{5} y^{8}}}{\sqrt{6 x y^{5}}}$ $sqrt(108x^5y^8)/sqrt(6xy^5)$ ?

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How do you simplify $\frac{\sqrt{108 x^{5} y^{8}}}{\sqrt{6 x y^{5}}}$ $sqrt(108x^5y^8)/sqrt(6xy^5)$ ?

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Answer 1 · 2016-05-11T20:45:14

$3 x^{2} \sqrt{2 y^{3}}$ $3x^2sqrt(2y^3)$

Explanation:

$\frac{\sqrt{108 x^{5} y^{8}}}{\sqrt{6 x y^{5}}} = \sqrt{\frac{108 x^{5} y^{8}}{6 x y^{5}}}$ $sqrt(108x^5y^8)/sqrt(6xy^5)=sqrt((108x^5y^8)/(6xy^5))$
$= \sqrt{(\frac{108}{6}) (\frac{x^{5}}{x}) (\frac{y^{8}}{y^{5}})}$ $=sqrt((108/6)(x^5/x)(y^8/y^5)$
$= \sqrt{(18) (x^{5 - 1}) (y^{8 - 5})}$ $=sqrt((18)(x^(5-1))(y^(8-5))$
$= \sqrt{(18) (x^{4}) (y^{3})}$ $=sqrt((18)(x^4)(y^3)$
$= 3 x^{2} \sqrt{2 y^{3}}$ $=3x^2sqrt(2y^3)$

Answer 2 · 2016-05-11T20:47:52

$3 x^{2} y \sqrt{2 y}$ $3x^2ysqrt(2y)$

Explanation:

Each square root can be calculated separately, or because it is a division, it can be combined into a single square root.

$\frac{\sqrt{108 x^{5} y^{8}}}{\sqrt{6 x y^{5}}}$ $sqrt(108x^5y^8)/sqrt(6xy^5)$ = $\sqrt{18 x^{4} y^{3}} = \sqrt{9 \times 2 x^{4} y^{2} y}$ $sqrt(18x^4y^3) = sqrt(9 xx 2x^4y^2 y )$

= $3 x^{2} y \sqrt{2 y}$ $3x^2ysqrt(2y)$

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How do you simplify $\frac{\sqrt{108 x^{5} y^{8}}}{\sqrt{6 x y^{5}}}$ $sqrt(108x^5y^8)/sqrt(6xy^5)$ ?

2 Answers

Explanation:

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How do you simplify $\frac{\sqrt{108 x^{5} y^{8}}}{\sqrt{6 x y^{5}}}$ $sqrt(108x^5y^8)/sqrt(6xy^5)$ ?