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

sqrt(2a)*sqrt(14a^(3))*sqrt(5a)=

Simplify. $\newline$ Multiply and remove all perfect squares from inside the square roots. Assume $\newline$ $a$ is positive. $\newline$ $\sqrt{2a}\cdot\sqrt{14a^{3}}\cdot\sqrt{5a}=$

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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

a

is positive.

\newline

\sqrt{2a}\cdot\sqrt{14a^{3}}\cdot\sqrt{5a}=

Multiply square roots: First, we need to multiply the square roots together. $\sqrt{2a} \times \sqrt{14a^3} \times \sqrt{5a} = \sqrt{2a \times 14a^3 \times 5a}$
Simplify expression under square root: Now, we simplify the expression under the square root by multiplying the numbers and combining the 'a' terms. $\newline$ $2a \times 14a^3 \times 5a = 2 \times 14 \times 5 \times a \times a^3 \times a$ $\newline$ $= 140 \times a^5$
Rewrite expression to identify perfect squares: Next, we rewrite the expression under the square root in a way that will help us identify perfect squares. $\newline$ $\sqrt{140 \cdot a^5} = \sqrt{4 \cdot 35 \cdot a^4 \cdot a}$
Take square root of perfect squares out: We can now take the square root of the perfect squares $4$ and $a^4$ out of the square root. $\newline$ $\sqrt{4 \times 35 \times a^4 \times a} = \sqrt{4} \times \sqrt{a^4} \times \sqrt{35a}$ $\newline$ $= 2 \times a^2 \times \sqrt{35a}$
Final simplified answer: Finally, we have simplified the expression by removing all perfect squares from inside the square roots. $\newline$ The final answer is $2a^2 \cdot \sqrt{35a}$ .

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