Evaluate Math Expression: $8^{2} + \sqrt{ 3^{2} } - 2\sqrt{36} -11$

This problem requires us to simplify a mathematical expression involving powers and square roots. We need to calculate the value of $8^{2} + \sqrt{ 3^{2} } - 2\sqrt{36} -11$. Let's break down each part of the expression.

Step-by-Step Calculation

We will evaluate each term individually before combining them:

1. Calculate the power: $8^{2}$ means $8 \times 8$. $8^{2} = 64$
2. Calculate the square root of a square: $\sqrt{ 3^{2} }$ is the square root of $3 \times 3$, which is $\sqrt{9}$. The square root of 9 is 3. $\sqrt{ 3^{2} } = \sqrt{9} = 3$
3. Calculate the square root: $\sqrt{36}$ is the number which, when multiplied by itself, equals 36. That number is 6. $\sqrt{36} = 6$
4. Multiply the square root result: We need to calculate $2 \times \sqrt{36}$. Since $\sqrt{36} = 6$, this becomes: $2\sqrt{36} = 2 \times 6 = 12$

Combine the Terms

Now substitute the calculated values back into the original expression:

Perform the addition and subtraction from left to right:

• First, add $64 + 3$: $64 + 3 = 67$
• Next, subtract 12 from the result: $67 - 12 = 55$
• Finally, subtract 11 from the result: $55 - 11 = 44$

Therefore, the value of the expression $8^{2} + \sqrt{ 3^{2} } - 2\sqrt{36} -11$ is 44.