Evaluating the Square Root Expression

The problem asks for the value of the expression: $ \sqrt{121} + \sqrt{0.0225} - \sqrt{5.76} $ We need to calculate each square root term individually and then combine them.

Calculating Individual Square Roots

• First Term: $ \sqrt{121} $ Since $11 \times 11 = 121$, we have $ \sqrt{121} = 11 $.
• Second Term: $ \sqrt{0.0225} $ We know $15 \times 15 = 225$. To get $0.0225$, we need $0.15 \times 0.15$. So, $ \sqrt{0.0225} = 0.15 $.
• Third Term: $ \sqrt{5.76} $ We know $24 \times 24 = 576$. To get $5.76$, we need $2.4 \times 2.4$. So, $ \sqrt{5.76} = 2.4 $.

Combining the Terms

Now, substitute the calculated values back into the original expression:

Final Calculation

Perform the addition and subtraction:

1. Add the first two terms: $ 11 + 0.15 = 11.15 $
2. Subtract the third term from the result: $ 11.15 - 2.4 = 8.75 $

Therefore, the value of the expression is $8.75$.