Question

sixth root of 2 times the square root of 5

Answer 1

To simplify the expression \( \sqrt[6]{2} \times \sqrt{5} \), we can express it using exponents:

1. Rewrite the sixth root and square root:
\[
\sqrt[6]{2} = 2^{1/6}
\]
\[
\sqrt{5} = 5^{1/2}
\]

2. Combine the expressions:
\[
\sqrt[6]{2} \times \sqrt{5} = 2^{1/6} \times 5^{1/2}
\]

The expression is now simplified as \( 2^{1/6} \times 5^{1/2} \).

If desired, you can also leave it in exponential form or write it as a single radical:
\[
\sqrt[6]{2} \times \sqrt{5} = \frac{\sqrt{5}}{\sqrt[6]{1}} \cdot \sqrt[6]{2^3} = \sqrt[6]{2^3 \cdot 5^3}
\]

However, both forms provide a valid representation. The most simplified exact form is:

\[
2^{1/6} \times 5^{1/2}
\]

If you need a numerical approximation, you would calculate:
\[
\approx 1.1225 \, \text{(approximately)}
\]