Evaluating the Square Root Expression

The question asks us to find the value of the mathematical expression $\frac{\sqrt{0.01}}{\sqrt{0.0025}}$. We need to simplify the square roots and then perform the division.

Step-by-Step Calculation

Step 1: Calculate the square root of the numerator

The numerator is $\sqrt{0.01}$. We need to find a number that, when multiplied by itself, equals $0.01$. We know that $0.1 \times 0.1 = 0.01$. Therefore,

$ \sqrt{0.01} = 0.1 $

Step 2: Calculate the square root of the denominator

The denominator is $\sqrt{0.0025}$. We need to find a number that, when multiplied by itself, equals $0.0025$. We know that $0.05 \times 0.05 = 0.0025$. Therefore,

$ \sqrt{0.0025} = 0.05 $

Step 3: Perform the division

Now we substitute the simplified values back into the original expression:

$ \frac{\sqrt{0.01}}{\sqrt{0.0025}} = \frac{0.1}{0.05} $

To simplify this fraction, we can multiply the numerator and the denominator by 100 to remove the decimals:

$ \frac{0.1 \times 100}{0.05 \times 100} = \frac{10}{5} $

Finally, we perform the division:

$ \frac{10}{5} = 2 $

Final Answer

The value of the expression $\frac{\sqrt{0.01}}{\sqrt{0.0025}}$ is 2.