Question

Which of the following is equivalent to 5 square root 13^3

Answer 1

For this case we must find an expression equivalent to the following:

$5 \sqrt {13 ^ 3}$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

In addition, we know that:

$13 ^ 3 = 13 ^ 2 * 13$

Rewriting the given expression we have:

$5 \sqrt {13 ^ 3} = 5 \sqrt {13 ^ 2 * 13} = 13 * 5 \sqrt {13} = 65 \sqrt {13}$

Answer:

$65 \sqrt {13}$