Finding the Value of the Square Root Expression

The question asks to evaluate the expression $\sqrt{121} + \sqrt{0.0196} - \sqrt{8.41}$. We need to calculate each square root term individually.

Calculating Individual Square Roots

• Calculate $\sqrt{121}$: Since $11 \times 11 = 121$, we have $\sqrt{121} = 11$.
• Calculate $\sqrt{0.0196}$: We find that $14 \times 14 = 196$. For the decimal part, $0.14 \times 0.14 = 0.0196$. Thus, $\sqrt{0.0196} = 0.14$.
• Calculate $\sqrt{8.41}$: We know $29 \times 29 = 841$. Adjusting for the decimal places, $2.9 \times 2.9 = 8.41$. Therefore, $\sqrt{8.41} = 2.9$.

Evaluating the Expression

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

$ \sqrt{121} + \sqrt{0.0196} - \sqrt{8.41} = 11 + 0.14 - 2.9 $

Perform the addition first:

$ 11 + 0.14 = 11.14 $

Next, perform the subtraction:

$ 11.14 - 2.9 = 8.24 $

The value of the expression is 8.24.