Question

simplify nth root radicals (type 1)
score: 0/5 penalty: none
question
simplify \\(\sqrt{25x^6}\\) completely given \\(x > 0\\).
answer attempt 1 out of 5

Explanation:

Step1: Simplify the square root of 25

The square root of 25 is a perfect square, so $\sqrt{25} = 5$ because $5 \times 5 = 25$.

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

Using the property of exponents $\sqrt{a^n}=a^{\frac{n}{2}}$ (for even roots and positive \(a\)), for \(x^6\) with \(x>0\), we have $\sqrt{x^6}=x^{\frac{6}{2}} = x^3$ since when we take the square root (which is the 2nd root), we divide the exponent by 2.

Step3: Combine the results

Multiply the results from Step 1 and Step 2. So $\sqrt{25x^6}=\sqrt{25}\times\sqrt{x^6}=5\times x^3 = 5x^3$.

Answer:

\(5x^3\)