How do you simplify $\frac{\sqrt{20 x^{4}} \sqrt{5 x}}{\sqrt{4 x^{3}}}$ $(sqrt(20x^4)sqrt(5x))/(sqrt(4x^3))$ ?

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How do you simplify $\frac{\sqrt{20 x^{4}} \sqrt{5 x}}{\sqrt{4 x^{3}}}$ $(sqrt(20x^4)sqrt(5x))/(sqrt(4x^3))$ ?

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Answer 1 · 2015-04-09T17:49:43

$\sqrt{20 x^{4}} = (2 x) (x) \cdot \sqrt{5}$ $sqrt(20x^4) = (2x)(x)*sqrt(5)$
$\sqrt{5 x} = \sqrt{5} \cdot \sqrt{x}$ $sqrt(5x) = sqrt(5)*sqrt(x)$
$\sqrt{4 x^{3}} = (2 x) \cdot \sqrt{x}$ $sqrt(4x^3) = (2x)*sqrt(x)$

So $\frac{\sqrt{20 x^{4}} \sqrt{5 x}}{\sqrt{4 x^{3}}}$ $(sqrt(20x^4)sqrt(5x))/sqrt(4x^3)$
can be written as
$\frac{(2 x) (x) (\sqrt{5}) (\sqrt{5}) (\sqrt{x})}{(2 x) (\sqrt{x})}$ $((2x)(x)(sqrt(5))(sqrt(5))(sqrt(x)))/((2x)(sqrt(x))$

Simplifying:
$((cancel(2x))(x)(sqrt(5))(sqrt(5))(cancel(sqrt(x))))/(cancel((2x))(cancel(sqrt(x)))$
and combining the two $sqrt(5)$ components:

$(sqrt(20x^4)sqrt(5x))/sqrt(4x^3) = 5x$

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How do you simplify $\frac{\sqrt{20 x^{4}} \sqrt{5 x}}{\sqrt{4 x^{3}}}$ $(sqrt(20x^4)sqrt(5x))/(sqrt(4x^3))$ ?

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