Question

question
simplify \\(\sqrt{144x^6}\\) completely given \\(x > 0\\).
answer attempt 1 out of 2

Explanation:

Step1: Simplify the square root of 144

The square root of 144 is a perfect square. We know that \( \sqrt{144} = 12 \) because \( 12\times12 = 144 \).

Step2: Simplify the square root of \( x^6 \)

For the variable part, we use the property of exponents \( \sqrt{a^n}=a^{\frac{n}{2}} \) (when \( a\gt0 \)). Here, \( n = 6 \), so \( \sqrt{x^6}=x^{\frac{6}{2}}=x^3 \) (since \( x\gt0 \), we don't have to consider the absolute value).

Step3: Combine the results

Now, we combine the results from Step 1 and Step 2. \( \sqrt{144x^6}=\sqrt{144}\times\sqrt{x^6}=12\times x^3 = 12x^3 \)

Answer:

\( 12x^3 \)