Question

`√(24n^3)` (simplify radical) please show work

Answer 1

`2n √(6n)`

Explanation:

`\sqrt{24n {}^(3) }`

Factor out the perfect square ⬜

`\sqrt{2 {}^(2) } * 6 {n}^(3)`

`\sqrt{ {2}^(2) } * 6n {}^(2) * n`

Please the square root is for the entire formula ⬆️⬆️⬆️

the root of the product is equals to the root of each Factor

`\sqrt{2 {}^(2) } \sqrt{n {}^(2) } √(6n)`

reduce the index of the radical and exponent with 2

`2 \sqrt{n {}^(2) } √(6n)`

`2n √(6n)`

Solution

2n square root 6n

`2n √(6n)`

Hope this helps.....

Answer 2

The answer is

`2n √(6n)`

Explanation:

`\sqrt{24 {n}^(3) }`

First of all factor out the perfect square out.

In this question the perfect squares are 4 and x²

So we have

`\sqrt{4 * {n}^(2) * 6n}`

Separate the radicals

That's

`√(4) * \sqrt{ {n}^(2) } * √(6n)`

Simplify

`√(4) = 2 \\ \sqrt{ {n}^(2) } = n`

So we have

`2 * n * √(6n)`

We have the final answer as

`2n √(6n)`

Hope this helps