Sure, let's evaluate the given expressions step by step.
### Part (a):
Evaluate [tex]\(\sqrt{45} \times \sqrt{20}\)[/tex]:
1. First, calculate the square root of 45:
[tex]\[
\sqrt{45} \approx 6.708203932499369
\][/tex]
2. Next, calculate the square root of 20:
[tex]\[
\sqrt{20} \approx 4.47213595499958
\][/tex]
3. Now, multiply the two square roots together:
[tex]\[
\sqrt{45} \times \sqrt{20} \approx 6.708203932499369 \times 4.47213595499958
\][/tex]
4. The result of the multiplication is:
[tex]\[
\sqrt{45} \times \sqrt{20} \approx 30.000000000000004
\][/tex]
So, the evaluation of [tex]\(\sqrt{45} \times \sqrt{20}\)[/tex] is approximately [tex]\(30.000000000000004\)[/tex].
### Part (b):
Evaluate [tex]\(\sqrt{147} \times \sqrt{243}\)[/tex]:
1. First, calculate the square root of 147:
[tex]\[
\sqrt{147} \approx 12.12435565298214
\][/tex]
2. Next, calculate the square root of 243:
[tex]\[
\sqrt{243} \approx 15.588457268119896
\][/tex]
3. Now, multiply the two square roots together:
[tex]\[
\sqrt{147} \times \sqrt{243} \approx 12.12435565298214 \times 15.588457268119896
\][/tex]
4. The result of the multiplication is:
[tex]\[
\sqrt{147} \times \sqrt{243} \approx 189.0
\][/tex]
So, the evaluation of [tex]\(\sqrt{147} \times \sqrt{243}\)[/tex] is approximately [tex]\(189.0\)[/tex].
Therefore, the final answers are:
1. [tex]\(\sqrt{45} \times \sqrt{20}\)[/tex] is approximately [tex]\(30.000000000000004\)[/tex].
2. [tex]\(\sqrt{147} \times \sqrt{243}\)[/tex] is approximately [tex]\(189.0\)[/tex].
