Sure, let's solve the given mathematical expressions step by step:
### 2. [tex]\(\sqrt{(3+7)^2 - 19}\)[/tex]
1. Start by calculating the expression inside the parentheses:
[tex]\[
3 + 7 = 10
\][/tex]
2. Next, square this result:
[tex]\[
10^2 = 100
\][/tex]
3. Subtract 19 from the squared value:
[tex]\[
100 - 19 = 81
\][/tex]
4. Finally, take the square root of the result:
[tex]\[
\sqrt{81} = 9.0
\][/tex]
### 4. [tex]\(\sqrt{91 + (5 + 11 - 13)^2}\)[/tex]
1. Begin by calculating the expression inside the parentheses:
[tex]\[
5 + 11 - 13 = 3
\][/tex]
2. Square this result:
[tex]\[
3^2 = 9
\][/tex]
3. Add 91 to the squared value:
[tex]\[
91 + 9 = 100
\][/tex]
4. Take the square root of the result:
[tex]\[
\sqrt{100} = 10.0
\][/tex]
### 7. [tex]\(\sqrt[3]{4 \times (7 + 5 - 8)^2}\)[/tex]
1. Start by calculating the expression inside the parentheses:
[tex]\[
7 + 5 - 8 = 4
\][/tex]
2. Square this result:
[tex]\[
4^2 = 16
\][/tex]
3. Multiply the squared value by 4:
[tex]\[
4 \times 16 = 64
\][/tex]
4. Finally, take the cube root of the result:
[tex]\[
\sqrt[3]{64} = 3.9999999999999996
\][/tex]
So, the final results are:
- For expression 2: [tex]\(9.0\)[/tex]
- For expression 4: [tex]\(10.0\)[/tex]
- For expression 7: [tex]\(3.9999999999999996\)[/tex]
