Question

square root of

180
^3square root of 38
pi(3.14)^2

Answer 1

To simplify the expression \( \sqrt{180} \times 3\sqrt{38} \times \pi(3.14)^2 \), we can break it down step by step.

First, simplify \( \sqrt{180} \):
\[
\sqrt{180} = \sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5} = 6\sqrt{5}
\]

Next, \( 3\sqrt{38} \) is already in its simplest form.

Now we can calculate \( \pi(3.14)^2 \):
\[
(3.14)^2 = 9.8596
\]
So, \( \pi(3.14)^2 \):

If using \( \pi \approx 3.14 \):
\[
3.14 \times 9.8596 \approx 31.0
\]

Now we combine everything:
\[
6\sqrt{5} \times 3\sqrt{38} \times \pi(3.14)^2
\]

Calculating the product of the coefficients and the square roots:
\[
= 6 \times 3 \times 31.0 \times \sqrt{5 \times 38}
\]

First, compute \( 5 \times 38 = 190 \), so:
\[
6 \times 3 = 18
\]
Finally,
\[
= 18 \times 31.0 \times \sqrt{190}
\]
\[
= 558.0 \times \sqrt{190}
\]

Therefore, the approximate value of \( \sqrt{180} \times 3\sqrt{38} \times \pi(3.14)^2 \) is:
\[
\approx 558.0 \times \sqrt{190}
\]

To get a numerical approximation, substitute \( \sqrt{190} \approx 13.784 \):
\[
558.0 \times 13.784 \approx 7704.672
\]

Hence, the final answer is approximately:
\[
\approx 7704.67
\]