Question

$\sqrt{\frac{72}{25}}$

Explanation:

Step1: Split root into numerator/denominator

$\sqrt{\frac{72}{25}} = \frac{\sqrt{72}}{\sqrt{25}}$

Step2: Simplify denominator root

$\sqrt{25} = 5$, so $\frac{\sqrt{72}}{5}$

Step3: Factor numerator root

$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2}$

Step4: Simplify $\sqrt{36}$

$\sqrt{36} = 6$, so $\sqrt{72} = 6\sqrt{2}$

Step5: Combine terms

$\frac{6\sqrt{2}}{5}$

Answer:

$\frac{6\sqrt{2}}{5}$