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

2 Answers

1 vote

√(48n^9)=√(16n^8\cdot3n)=√(16n^8)\cdot√(3n)=4n^4√(3n)
User Laksys
by
8.6k points
5 votes

Answer:


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)

User Prince Hernandez
by
7.9k points