Sure, let's go through each expression step-by-step to find their solutions.
### Step-by-Step Solutions:
#### Individual Square Root Expressions:
1. [tex]\(2 \sqrt{45}\)[/tex]
[tex]\[
2 \sqrt{45} = 2 \times 6.708203932499369 \approx 13.416407864998739
\][/tex]
2. [tex]\(6 \sqrt{81}\)[/tex]
[tex]\[
6 \sqrt{81} = 6 \times 9 = 54.0
\][/tex]
3. [tex]\(-7 \sqrt{99}\)[/tex]
[tex]\[
-7 \sqrt{99} = -7 \times 9.9498743710662 \approx -69.6491205974634
\][/tex]
4. [tex]\(12 \sqrt{24}\)[/tex]
[tex]\[
12 \sqrt{24} = 12 \times 4.898979485566356 \approx 58.78775382679627
\][/tex]
5. [tex]\(10 \sqrt{200}\)[/tex]
[tex]\[
10 \sqrt{200} = 10 \times 14.142135623730951 \approx 141.4213562373095
\][/tex]
6. [tex]\(\sqrt{-108}\)[/tex] (Note: Since the square root of a negative number is imaginary, we denote it using 'i'.)
[tex]\[
\sqrt{-108} = \sqrt{108} \times i = 10.392304845413264i
\][/tex]
7. [tex]\(0.9 \sqrt{86}\)[/tex]
[tex]\[
0.9 \sqrt{86} = 0.9 \times 9.273618495495704 \approx 8.346256645946134
\][/tex]
8. [tex]\(2 \sqrt{131}\)[/tex]
[tex]\[
2 \sqrt{131} = 2 \times 11.445523142259598 \approx 22.891046284519195
\][/tex]
#### Exercise 2 Assignments:
1. [tex]\(-24 \sqrt{35} + 16 \sqrt{35}\)[/tex]
[tex]\[
-24 \sqrt{35} + 16 \sqrt{35} = (-24 + 16) \sqrt{35} = -8 \sqrt{35} \approx -47.328638264796936
\][/tex]
2. [tex]\(\frac{\sqrt{28}}{-\sqrt{96}}\)[/tex]
[tex]\[
\frac{\sqrt{28}}{-\sqrt{96}} = \frac{2 \sqrt{7}}{-4 \sqrt{6}} = \frac{\sqrt{7}}{-2 \sqrt{6}} = \frac{\sqrt{7}}{-2 \cdot \sqrt{6}} \approx -0.5400617248673217
\][/tex]
3. [tex]\(42 \sqrt{2} - 32 \sqrt{3} - 12 \sqrt{2}\)[/tex]
[tex]\[
42 \sqrt{2} - 32 \sqrt{3} - 12 \sqrt{2} = (42 - 12) \sqrt{2} - 32 \sqrt{3} = 30 \sqrt{2} - 32 \sqrt{3} \approx -12.999218971011217
\][/tex]
Thus, these are the detailed step-by-step solutions for the given problems.
