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

3sqrt(5a)*8sqrt(35a^(2))=

Simplify. $\newline$ Multiply and remove all perfect squares from inside the square roots. Assume $\newline$ $a$ is positive. $\newline$ $3\sqrt{5a} \times 8\sqrt{35a^{2}}=$

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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

3\sqrt{5a} \times 8\sqrt{35a^{2}}=

Multiply coefficients: Multiply the coefficients (numbers outside the square roots) together. $\newline$ $3 \times 8 = 24$
Multiply radicands: Multiply the radicands (numbers inside the square roots) together. $\sqrt{5a} \times \sqrt{35a^2} = \sqrt{5a \times 35a^2}$
Simplify expression inside square root: Simplify the expression inside the square root. $5a \times 35a^2 = 175a^3$
Factor expression inside square root: Factor the expression inside the square root to identify perfect squares. $\newline$ $175a^3 = 5 \times 5 \times 7 \times a \times a \times a = (5^2) \times 7 \times (a^2) \times a$
Take square root of perfect squares: Take the square root of the perfect squares. $\sqrt{(5^2) \cdot 7 \cdot (a^2) \cdot a} = 5a \cdot \sqrt{7a}$
Multiply result by coefficient: Multiply the result from Step $5$ by the coefficient from Step $1$ . $\newline$ $24 \times (5a \times \sqrt{7a}) = 120a \times \sqrt{7a}$

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