To calculate [tex]\(\sqrt{\frac{5}{2}} \times \sqrt{40}\)[/tex], we can proceed as follows:
1. Combine the square roots:
Notice that we can use the property of square roots, [tex]\(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\)[/tex].
So,
[tex]\[
\sqrt{\frac{5}{2}} \times \sqrt{40} = \sqrt{\left(\frac{5}{2} \times 40\right)}
\][/tex]
2. Simplify inside the square root:
Multiply [tex]\(\frac{5}{2}\)[/tex] by [tex]\(40\)[/tex]:
[tex]\[
\frac{5}{2} \times 40 = \frac{5 \times 40}{2} = \frac{200}{2} = 100
\][/tex]
3. Calculate the square root of the result:
Now, take the square root of [tex]\(100\)[/tex]:
[tex]\[
\sqrt{100} = 10
\][/tex]
Therefore, the final result of [tex]\(\sqrt{\frac{5}{2}} \times \sqrt{40}\)[/tex] is:
[tex]\[
\boxed{10}
\][/tex]
