Question

multiply and simplify. assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers.$sqrt{6x^{6}} cdot sqrt{12x^{3}}$$sqrt{6x^{6}} cdot sqrt{12x^{3}} = square$(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine radicals into one

$\sqrt{6x^6 \cdot 12x^3}$

Step2: Multiply radicand terms

$\sqrt{(6 \cdot 12) \cdot (x^6 \cdot x^3)} = \sqrt{72x^9}$

Step3: Factor into perfect squares

$\sqrt{36 \cdot 2 \cdot x^8 \cdot x}$

Step4: Simplify perfect square radicals

$\sqrt{36} \cdot \sqrt{x^8} \cdot \sqrt{2x} = 6x^4\sqrt{2x}$

Answer:

$6x^4\sqrt{2x}$