Question

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

Answer 1

Answer:

$4n^4\sqrt{3n}$

Step-by-step explanation:

Use the exponent rules:

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

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

To find the simplified form of :

$\sqrt{48n^9}$

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;

$\sqrt{4^2 \cdot 3 \cdot (n^4)^2 \cdot n}$

Apply the exponent rule:

⇒$4 \cdot n^4 \cdot \sqrt{3n}$

⇒$4n^4\sqrt{3n}$

Therefore, the simplified form of square root 48n^9 is, $4n^4\sqrt{3n}$

Answer 2

$\sqrt{48n^9}=\sqrt{16n^8\cdot3n}=\sqrt{16n^8}\cdot\sqrt{3n}=4n^4\sqrt{3n}$