Question

which expression is equivalent to \\(\sqrt{\frac{36}{25}}\\)?
options: \\(\frac{6}{25}\\), \\(\frac{5}{6}\\), \\(\frac{6}{5}\\), \\(\frac{36}{25}\\)

Explanation:

Step1: Recall square root property

The square root of a fraction is the fraction of the square roots, i.e., $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ for $a\geq0, b>0$.
So, $\sqrt{\frac{36}{25}}=\frac{\sqrt{36}}{\sqrt{25}}$.

Step2: Calculate square roots

We know that $\sqrt{36} = 6$ (since $6\times6 = 36$) and $\sqrt{25}=5$ (since $5\times5 = 25$).
Thus, $\frac{\sqrt{36}}{\sqrt{25}}=\frac{6}{5}$.

Answer:

$\frac{6}{5}$ (assuming the third option is $\frac{6}{5}$ based on the visible numerator and denominator in the options)