Certainly! Let's go through the mathematical expression step by step:
Given expression:
[tex]$(\sqrt{9})^2 \cdot (\sqrt[3]{4})^3 \div 4 + \sqrt{49} \cdot \sqrt{4} - (11)^2$[/tex]
1. Simplify the square root and powers:
- The term [tex]$(\sqrt{9})^2$[/tex] can be simplified as follows:
[tex]\[
\sqrt{9} = 3 \implies (\sqrt{9})^2 = 3^2 = 9
\][/tex]
2. Simplify the cube root and powers:
- The term [tex]$(\sqrt[3]{4})^3$[/tex] is simplified by finding the cube root and raising it to the power of 3:
[tex]\[
\sqrt[3]{4} \approx 1.5874 \implies (\sqrt[3]{4})^3 \approx 1.5874^3 = 4
\][/tex]
3. Perform the division:
- Next, divide the result from the previous step by 4:
[tex]\[
4 \div 4 = 1
\][/tex]
4. Simplify the square root product:
- Now, simplify [tex]$\sqrt{49} \cdot \sqrt{4}$[/tex]:
[tex]\[
\sqrt{49} = 7 \quad \text{and} \quad \sqrt{4} = 2 \implies 7 \cdot 2 = 14
\][/tex]
5. Simplify the square of 11:
- Calculate [tex]$(11)^2$[/tex]:
[tex]\[
11^2 = 121
\][/tex]
6. Combine and simplify the terms:
- Now, put everything together:
[tex]\[
(\sqrt{9})^2 \cdot (\sqrt[3]{4})^3 \div 4 + \sqrt{49} \cdot \sqrt{4} - (11)^2 = 9 \cdot 1 + 14 - 121
\][/tex]
- Simplify the expression step-by-step:
[tex]\[
9 \cdot 1 = 9
\][/tex]
[tex]\[
9 + 14 = 23
\][/tex]
[tex]\[
23 - 121 = -98
\][/tex]
Thus, the value of the given expression is:
[tex]$ -98 $[/tex]
