Question

simplify.
multiply and remove all perfect squares from inside the square roots. assume x is positive.
\sqrt{3x^4} \cdot \sqrt{5x^2} \cdot \sqrt{10} = \square

Explanation:

Step1: Combine square roots

$\sqrt{3x^4} \cdot \sqrt{5x^2} \cdot \sqrt{10} = \sqrt{3x^4 \cdot 5x^2 \cdot 10}$

Step2: Multiply terms inside root

$\sqrt{3 \cdot 5 \cdot 10 \cdot x^4 \cdot x^2} = \sqrt{150x^6}$

Step3: Factor into perfect squares

$\sqrt{25 \cdot 6 \cdot (x^3)^2} = \sqrt{25} \cdot \sqrt{(x^3)^2} \cdot \sqrt{6}$

Step4: Simplify perfect square roots

$5 \cdot x^3 \cdot \sqrt{6} = 5x^3\sqrt{6}$

Answer:

$5x^3\sqrt{6}$