Question

simplify this radical.\\(sqrt{x^{13}}\\)\\(13sqrt{x}\\)\\(x^{6}sqrt{x}\\)\\(6xsqrt{x}\\)\\(xsqrt{x^{12}}\\)

Explanation:

Step1: Split exponent into even + odd

$\sqrt{x^{13}} = \sqrt{x^{12} \cdot x}$

Step2: Separate radicals using product rule

$\sqrt{x^{12} \cdot x} = \sqrt{x^{12}} \cdot \sqrt{x}$

Step3: Simplify $\sqrt{x^{12}}$

$\sqrt{x^{12}} = x^6$

Step4: Combine terms

$x^6 \cdot \sqrt{x} = x^6\sqrt{x}$

Answer:

$\boldsymbol{x^6\sqrt{x}}$