How do you simplify $\sqrt{\frac{9}{50 x y^{7}}}$ $sqrt ( 9 /( 50xy^7))$ ?

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How do you simplify $\sqrt{\frac{9}{50 x y^{7}}}$ $sqrt ( 9 /( 50xy^7))$ ?

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Answer 1 · 2017-07-18T08:32:57

$= \frac{3 \sqrt{2 x y}}{10 x y^{4}}$ $= (3sqrt(2xy))/(10xy^4$

Explanation:

Write the numbers as a product of their factors, using squares where possible.

Find roots where possible.

$\sqrt{\frac{9}{50 x y^{7}}} = \sqrt{\frac{3 \times 3}{2 \times 5 \times 5 x y y^{6}}}$ $sqrt(9/(50xy^7)) " "= sqrt((3xx3)/(2xx5xx5 x y y^6)$

$= \frac{3}{5 y^{3}} \sqrt{\frac{1}{2 x y}} = \frac{3}{5 y^{3}} \frac{1}{\sqrt{2 x y}} = \frac{3}{5 y^{3} \sqrt{2 x y}}$ $=3/(5y^3)sqrt(1/(2xy))" " =3/(5y^3)1/(sqrt(2xy)) " "= 3/(5y^3sqrt(2xy))$

You will probably want to rationalise the denominator

$\frac{3}{5 y^{3} \sqrt{2 x y}} \times \frac{\sqrt{2 x y}}{\sqrt{2 x y}}$ $3/(5y^3sqrt(2xy)) xx sqrt(2xy)/sqrt(2xy)$

$= \frac{3 \sqrt{2 x y}}{5 y^{3} \times 2 x y}$ $=(3sqrt(2xy))/(5y^3 xx 2xy)$

$= \frac{3 \sqrt{2 x y}}{10 x y^{4}}$ $= (3sqrt(2xy))/(10xy^4$

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How do you simplify $\sqrt{\frac{9}{50 x y^{7}}}$ $sqrt ( 9 /( 50xy^7))$ ?

1 Answer

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