Question

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

Answer 1

`√(15)^3 = 15 √(15)`

Explanation:

Given

`√(15)^3`

Required

Simplify

`√(15)^3`

Apply the following law of indices:

`x^3 = x * x * x`

So, we have:

`√(15)^3 = √(15) * √(15) * √(15)`

Combine two terms

`√(15)^3 = √(15 * 15) * √(15)`

`√(15)^3 = √(225) * √(15)`

Take positive square root of 225

`√(15)^3 = 15 * √(15)`

`√(15)^3 = 15 √(15)`

Hence:

The solution to
`√(15)^3` is
`15\sqrt{15`