Question

write the following in terms of the simplest possible surds.
15/^3​

Answer 1

Answer:

$\sqrt{15}^3 = 15 \sqrt{15}$

Step-by-step explanation:

Given

$\sqrt{15}^3$

Required

Simplify

$\sqrt{15}^3$

Apply the following law of indices:

$x^3 = x * x * x$

So, we have:

$\sqrt{15}^3 = \sqrt{15} * \sqrt{15} * \sqrt{15}$

Combine two terms

$\sqrt{15}^3 = \sqrt{15 * 15} * \sqrt{15}$

$\sqrt{15}^3 = \sqrt{225} * \sqrt{15}$

Take positive square root of 225

$\sqrt{15}^3 = 15 * \sqrt{15}$

$\sqrt{15}^3 = 15 \sqrt{15}$

Hence:

The solution to $\sqrt{15}^3$ is $15\sqrt{15$