Question

which expression is equivalent to radical 31x^6

Answer 1

To simplify the expression \(\sqrt{31x^6}\), we can separate the constant and the variable parts:

\[
\sqrt{31x^6} = \sqrt{31} \cdot \sqrt{x^6}
\]

Next, we simplify \(\sqrt{x^6}\). Since \(x^6\) is a perfect square, we can take the square root:

\[
\sqrt{x^6} = x^{6/2} = x^3
\]

So, combining both parts, we have:

\[
\sqrt{31x^6} = \sqrt{31} \cdot x^3
\]

Thus, the expression equivalent to \(\sqrt{31x^6}\) is:

\[
x^3\sqrt{31}
\]