Simplify $3 \sqrt{\frac{125}{36}}$ $3sqrt(125/36)$ ?

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Answer 1 · 2017-03-29T03:53:22

$\frac{5 \sqrt{5}}{2}$ $(5sqrt(5))/2$

I'm reading this as $3 \sqrt{\frac{125}{36}}$ $3sqrt(125/36)$

First thing to do is see that we can rewrite the terms under the square root sign into terms that have perfect squares:

$3 \sqrt{\frac{5 \times 25}{36}}$ $3sqrt((5xx25)/36)$

$3 (\frac{\sqrt{5} \times \sqrt{25}}{\sqrt{36}})$ $3((sqrt(5)xxsqrt(25))/sqrt36)$

Let's take square roots of the perfect squares:

$3 \times \frac{\sqrt{5} \times 5}{6}$ $3xx(sqrt(5)xx5)/6$

$\frac{3 \times \sqrt{5} \times 5}{6}$ $(3xxsqrt(5)xx5)/6$

Let's cancel the 6 in the denominator against the 3 in the numerator and reorder the terms:

$\frac{5 \sqrt{5}}{2}$ $(5sqrt(5))/2$

Simplify 3sqrt(125/36)3√125363sqrt(125/36)?