How do you simplify $\frac{\sqrt{2 b^{5}}}{\sqrt{14 c^{2}}}$ $sqrt(2b^5)/sqrt(14c^2)$ ?

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Answer 1 · 2017-04-25T05:00:39

See below.

As you can see, you can't just directly take the square root and be done, or you wouldn't be simplifying correctly. Here is what I would do:

$\frac{\sqrt{2 b^{5}}}{\sqrt{14 c^{2}}}$ $sqrt(2b^5)/sqrt(14c^2)$

$\frac{\sqrt{2 b \cdot b^{2} \cdot b^{2}}}{\sqrt{14 \cdot c \cdot c}}$ $sqrt(2b * b^2 * b^2)/ sqrt(14 * c * c)$

$\frac{b^{2} \sqrt{2 b}}{c \sqrt{14}}$ $(b^2sqrt(2b))/(csqrt(14))$

$\frac{b^{2} \sqrt{2} \cdot \sqrt{b}}{c \cdot \sqrt{2} \cdot \sqrt{7}}$ $(b^2sqrt(2)* sqrt(b))/(c* sqrt(2)* sqrt(7))$

$\frac{b^{2} \cdot \sqrt{b}}{c \cdot \sqrt{7}}$ $(b^2 * sqrt(b))/(c * sqrt(7))$

$\frac{b^{2} \sqrt{b}}{c \sqrt{7}}$ $(b^2 sqrt(b))/(c sqrt(7))$

This would be your final answer.

I hope that helps!

How do you simplify √2b5√14c2sqrt(2b^5)/sqrt(14c^2)?