Certainly! Let's solve the expression [tex]\(\sqrt{20} \times (\sqrt{5})^3\)[/tex] step by step:
1. Finding [tex]\(\sqrt{20}\)[/tex]:
The square root of 20 ([tex]\(\sqrt{20}\)[/tex]) can be computed as:
[tex]\[
\sqrt{20} = 4.47213595499958
\][/tex]
2. Finding [tex]\((\sqrt{5})^3\)[/tex]:
First, we need to find the square root of 5 ([tex]\(\sqrt{5}\)[/tex]), then raise it to the power of 3.
The square root of 5 is:
[tex]\[
\sqrt{5} = 2.23606797749979
\][/tex]
Raising [tex]\(\sqrt{5}\)[/tex] to the power of 3:
[tex]\[
(\sqrt{5})^3 = (2.23606797749979)^3 = 11.18033988749895
\][/tex]
3. Multiplying the Results:
Finally, we multiply [tex]\(\sqrt{20}\)[/tex] by [tex]\((\sqrt{5})^3\)[/tex]:
[tex]\[
\sqrt{20} \times (\sqrt{5})^3 = 4.47213595499958 \times 11.18033988749895 = 50.000000000000014
\][/tex]
Therefore, the result of the expression [tex]\(\sqrt{20} \times (\sqrt{5})^3\)[/tex] is [tex]\(50.000000000000014\)[/tex].
