$$ The Value of  √169 + √ 0.0144 - √ 5.76

The correct option is 10.72.

Let's break down the given expression step-by-step to evaluate its value.

The given mathematical expression is:

$169+0.0144-5.76$

Step 1: Calculate the square root of each term individually.

1. Evaluate $\sqrt{169}$:

Since 13 × 13 = 169, we have:

$169=13$

2. Evaluate $\sqrt{0.0144}$:

We can write 0.0144 as a fraction: $\frac{144}{10000}$.

Taking the square root gives:

$0.0144=\frac{144}{10000}=\frac{12}{100}=0.12$

3. Evaluate $\sqrt{5.76}$:

We can write 5.76 as a fraction: $\frac{576}{100}$.

Taking the square root gives:

$5.76=\frac{576}{100}=\frac{24}{10}=2.4$

Step 2: Substitute the calculated values back into the expression.

$13+0.12-2.4$

Step 3: Perform addition and subtraction.

First, add 13 and 0.12:

$13+0.12=13.12$

Now, subtract 2.4 from 13.12:

$13.12-2.4=10.72$

Thus, the final value of the given expression is 10.72.