Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume $x$ is positive.
$$
\sqrt{3 x^{4}} \cdot \sqrt{5 x^{2}} \cdot \sqrt{10}=
$$
$\square$

Question

Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume $x$ is positive.
$$
\sqrt{3 x^{4}} \cdot \sqrt{5 x^{2}} \cdot \sqrt{10}=
$$
$\square$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Combine the square roots into a single square root by multiplying the expressions under the radicals. ‖ ‖ step 2 ⋮ Simplify the expression under the square root: $ \sqrt{3x^4} \cdot \sqrt{5x^2} \cdot \sqrt{10} = \sqrt{3 \cdot 5 \cdot 10 \cdot x^4 \cdot x^2} $. ‖ ‖ step 3 ⋮ Calculate the product under the square root: $ \sqrt{150 \cdot x^6} $. ‖ ‖ step 4 ⋮ Factor out the perfect squares from under the square root: $ \sqrt{150 \cdot x^6} = \sqrt{25 \cdot 6 \cdot x^4 \cdot x^2} $. ‖ ‖ step 5 ⋮ Take the square root of the perfect squares: $ \sqrt{25} \cdot \sqrt{x^4} \cdot \sqrt{x^2} = 5x^2 \cdot x $. ‖ ‖ step 6 ⋮ Simplify the expression: $ 5x^2 \cdot x = 5x^3 $. ‖ ‖ step 7 ⋮ Multiply the remaining square root by the simplified expression: $ 5x^3 \cdot \sqrt{6} $. ‖ ∻Answer∻ ⚹ $5x^3 \sqrt{6}$ ⚹ ∻Key Concept∻ ⚹Simplifying Square Roots⚹ ∻Explanation∻ ⚹When simplifying the product of several square roots, combine them into a single square root, factor out perfect squares, and then take the square root of those perfect squares. The remaining square root is multiplied by the simplified expression outside the square root.⚹◊What is the simplified form of $\sqrt{3x^{4}} \cdot \sqrt{5x^{2}} \cdot \sqrt{10}$?⍭ Generate me a similar question◊

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