Solve Nested Square Roots: √√(100/25) × √√25 Multiplication Problem

Solve the following exercise:

$\sqrt{\sqrt{\frac{100}{25}}}\cdot\sqrt{\sqrt{25}}=$

To solve this problem, let's evaluate the expression $\sqrt{\sqrt{\frac{100}{25}}} \cdot \sqrt{\sqrt{25}}$ step-by-step.

Step 1: Simplify $\sqrt{\frac{100}{25}}$.
We calculate $\frac{100}{25}$, which simplifies to 4. Therefore, $\sqrt{\frac{100}{25}} = \sqrt{4} = 2$.

Step 2: Now find $\sqrt{\sqrt{4}}$.
$\sqrt{4} = 2$, so $\sqrt{2}$ remains as it is.

Step 3: Simplify $\sqrt{\sqrt{25}}$.
Note that $\sqrt{25} = 5$. Therefore, $\sqrt{\sqrt{25}} = \sqrt{5}$.

Step 4: Combine the results:
The expression simplifies to $\sqrt{2} \cdot \sqrt{5}$, which is equal to $\sqrt{2 \cdot 5} = \sqrt{10}$.

Thus, the final result of the expression is $\sqrt{10}$.

The correct choice from the options provided is: $\sqrt{10}$.