How to simplify this?

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How to simplify this?

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Answer 1 · 2017-08-31T11:37:14

$\frac{6 x^{3} y^{3} \sqrt{15 y}}{\sqrt{5 x y}}$ $(6x^3y^3sqrt(15y))/sqrt(5xy)$

Explanation:

I am assuming the 3 before the radical in the numerator is not representing the 3rd root and the 12 is not a multiplier but a question number. If this is not the case then answer will be incorrect.

(1.) Factor the radicand in the numerator so you can extract roots.

$3 \sqrt{60 x^{6} y^{9}}$ $3sqrt(60x^6y^9)$ can be factored as

$3 \sqrt{4 \cdot 15 \cdot x^{6} \cdot y^{8} \cdot y}$ $3sqrt(4* 15 *x^6 *y^8 *y)$

(2.) Extract roots. It can be seen for example that the root of $x^{6}$ $x^6$ is $x^{3}$ $x^3$ , since $x^{3} \cdot x^{3} \Rightarrow x^{6}$ $x^3 * x^3 => x^6$ and root of $y^{8}$ $y^8$ is $y^{4}$ $y^4$ since $y^{4} \cdot y^{4} \Rightarrow y^{8}$ $y^4 * y^4 => y^8$ .

$6 x^{3} y^{4} \sqrt{15 y}$ $6x^3y^4sqrt(15y)$

(3.) Do the same with the denominator.

$\sqrt{5 x y^{3}} \Rightarrow \sqrt{5 \cdot x \cdot y^{2} \cdot y} \Rightarrow y \sqrt{5 x y}$ $sqrt(5xy^3) => sqrt(5 * x * y^2 * y) => ysqrt(5xy)$

$\frac{6 x^{3} y^{4} \sqrt{15 y}}{y \sqrt{5 x y}}$ $(6x^3y^4sqrt(15y))/(ysqrt(5xy)$

(4.) Cancelling like factors gives:

$\frac{6 x^{3} y^{3} \sqrt{15 y}}{\sqrt{5 x y}}$ $(6x^3y^3sqrt(15y))/sqrt(5xy)$

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