Question

which expression is equivalent to \\(sqrt{\frac{36}{25}}\\)?

Explanation:

Step1: Recall square root property

The property of square roots states that $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ for $a\geq0$ and $b > 0$.

Step2: Apply the property to the given expression

Given the expression $\sqrt{\frac{36}{25}}$, using the above property, we can rewrite it as $\frac{\sqrt{36}}{\sqrt{25}}$.

Step3: Calculate the square roots

We know that $\sqrt{36} = 6$ and $\sqrt{25}=5$. So $\frac{\sqrt{36}}{\sqrt{25}}=\frac{6}{5}$.
Now we need to check which of the options (even though the options are a bit unclear from the image, but from the structure, we assume the correct one is the one equal to $\frac{6}{5}$ or $\frac{\sqrt{36}}{\sqrt{25}}$) matches. If one of the options is $\frac{6}{5}$ (or $\frac{\sqrt{36}}{\sqrt{25}}$), that is the equivalent expression.

Answer:

Assuming the options include $\frac{6}{5}$ (or $\frac{\sqrt{36}}{\sqrt{25}}$), the equivalent expression is $\frac{6}{5}$ (or $\frac{\sqrt{36}}{\sqrt{25}}$ depending on the option format). If we consider the first option (assuming the first option is $\frac{6}{5}$ or similar), the correct option would be the one with $\frac{6}{5}$ (e.g., if the first option is $\frac{6}{5}$, then A. $\frac{6}{5}$).