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, \(4n^4\sqrt{3n}\)