How do you simplify $\sqrt{\frac{5 c^{5}}{4 d^{5}}}$ $sqrt((5c^5)/(4d^5))$ ?

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How do you simplify $\sqrt{\frac{5 c^{5}}{4 d^{5}}}$ $sqrt((5c^5)/(4d^5))$ ?

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Answer 1 · 2016-09-20T18:33:28

$\frac{c^{2} \sqrt{5 c d}}{2 d^{3}}$ $" "color(brown)((c^2sqrt(5cd))/(2d^3))$

Explanation:

Write as: $\frac{\sqrt{5 c^{5}}}{\sqrt{4 d^{5}}} = \frac{\sqrt{5 \times c^{2} \times c^{2} \times c}}{\sqrt{2^{2} \times d^{2} \times d^{2} \times d}}$ $" "sqrt(5c^5)/sqrt(4d^5)" "=" "sqrt(5xxc^2xxc^2xxc)/(sqrt(2^2xxd^2xxd^2xxd)$

$= \frac{c^{2} \sqrt{5 c}}{2 d^{2} \sqrt{d}}$ $=(c^2sqrt(5c))/(2d^2sqrt(d))$

$= \frac{c^{2} \sqrt{5 c}}{2 d^{2} \sqrt{d}} \times 1 = \frac{c^{2} \sqrt{5 c}}{2 d^{2} \sqrt{d}} \times \frac{\sqrt{d}}{\sqrt{d}}$ $=(c^2sqrt(5c))/(2d^2sqrt(d))color(magenta)(xx1)" " =" "(c^2sqrt(5c))/(2d^2sqrt(d))color(magenta)(xxsqrtd/sqrtd)$

$= \frac{c^{2} \sqrt{5 c d}}{2 d^{3}}$ $=(c^2sqrt(5cd))/(2d^3)$

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How do you simplify $\sqrt{\frac{5 c^{5}}{4 d^{5}}}$ $sqrt((5c^5)/(4d^5))$ ?

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