Question 13 of 16
Simplify the radical. Assume that all variables represent positive numbers.
\[
\sqrt{48 x^{12}}
\]
\[
\sqrt{48 x^{12}}=\square
\]
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answer
Final Answer: \(\sqrt{48 x^{12}} = \boxed{4\sqrt{3}x^6}\)
Step 1 ：The given expression is \(\sqrt{48 x^{12}}\).
Step 2 ：To simplify this, we need to break down the number 48 into its prime factors and simplify the power of x.
Step 3 ：The prime factorization of 48 is \(2^4 * 3\).
Step 4 ：The power of x can be simplified by dividing the exponent by 2, since we are taking the square root.
Step 5 ：The simplified expression is \(4\sqrt{3}x^6\). This is because the square root of \(x^{12}\) is \(x^6\) and the square root of 48 is \(4\sqrt{3}\).
Step 6 ：Final Answer: \(\sqrt{48 x^{12}} = \boxed{4\sqrt{3}x^6}\)
