Question

simplify. assume that the variable represents a nonnegative real number. $sqrt{121x^{5}}$ $sqrt{121x^{5}} = square$ (type an exact answer, using radicals as needed.)

Explanation:

Step1: Split radical into product

$\sqrt{121x^5} = \sqrt{121} \cdot \sqrt{x^5}$

Step2: Simplify $\sqrt{121}$

$\sqrt{121} = 11$

Step3: Rewrite $x^5$ as $x^4 \cdot x$

$\sqrt{x^5} = \sqrt{x^4 \cdot x} = \sqrt{x^4} \cdot \sqrt{x}$

Step4: Simplify $\sqrt{x^4}$

$\sqrt{x^4} = x^2$ (since $x \geq 0$)

Step5: Combine all simplified terms

$11 \cdot x^2 \cdot \sqrt{x} = 11x^2\sqrt{x}$

Answer:

$11x^2\sqrt{x}$