Question

What is the simplified form of square root 48n^9?

Answer 1

`√(48n^9)=√(16n^8\cdot3n)=√(16n^8)\cdot√(3n)=4n^4√(3n)`

Answer 2

`4n^4√(3n)`

Explanation:

Use the exponent rules:

`\sqrt[n]{x^a} = x^{(a)/(n)}`

`\sqrt[n]{a^n} =a`

To find the simplified form of :

`√(48n^9)`

We can write 48 and
`n^9` as:

`48 = 4 \cdot 4 \cdot 3 = 4^2 \cdot 3`

`n^9 = (n^4)^2 \cdot n`

then;

`√(4^2 \cdot 3 \cdot (n^4)^2 \cdot n)`

Apply the exponent rule:

⇒
`4 \cdot n^4 \cdot √(3n)`

⇒
`4n^4√(3n)`

Therefore, the simplified form of square root 48n^9 is,
`4n^4√(3n)`