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Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume
x is positive.

sqrt(3x^(4))*sqrt(5x^(2))*sqrt10=

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

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Multiply and remove all perfect squares from inside the square roots. Assume

\newline

x

is positive.

\newline

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

Multiply square roots: We start by multiplying the square roots together, using the property that $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ . $\newline$ $\sqrt{3x^{4}}\times\sqrt{5x^{2}}\times\sqrt{10} = \sqrt{3x^{4} \times 5x^{2} \times 10}$
Combine terms under square root: Next, we combine the terms under the single square root. $\sqrt{3x^{4} \cdot 5x^{2} \cdot 10} = \sqrt{15x^{6} \cdot 10} = \sqrt{150x^{6}}$
Identify perfect squares: Now we look for perfect squares within the square root. We can see that $150$ can be factored into $2 \times 3 \times 5^2$ , and $x^{6}$ is a perfect square since $6$ is an even exponent. $\newline$ $\sqrt{150x^{6}} = \sqrt{2 \times 3 \times 5^2 \times x^{6}}$
Take out perfect squares: We can now take out the perfect squares from under the square root. $\sqrt{2 \cdot 3 \cdot 5^2 \cdot x^{6}} = 5 \cdot x^{3} \cdot \sqrt{2 \cdot 3}$
Simplify expression: Finally, we simplify the expression under the square root. $\sqrt{2 \times 3} = \sqrt{6}$ So, the final simplified expression is $5 \times x^{3} \times \sqrt{6}$ .

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