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

6sqrt(15y^(4))*2sqrt(20y^(2))=

Simplify. $\newline$ Multiply and remove all perfect squares from inside the square roots. Assume $\newline$ $y$ is positive. $\newline$ $6\sqrt{15y^{4}}\times2\sqrt{20y^{2}}=$

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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

y

is positive.

\newline

6\sqrt{15y^{4}}\times2\sqrt{20y^{2}}=

Write expression: Write down the expression to be simplified. $\newline$ We have the expression $6\sqrt{15y^{4}} \cdot 2\sqrt{20y^{2}}$ .
Multiply coefficients: Multiply the coefficients (numbers outside the square roots) together. $6 \times 2 = 12$
Multiply radicands: Multiply the radicands (numbers inside the square roots) together. $\sqrt{15y^{4}} \times \sqrt{20y^{2}} = \sqrt{15 \times 20 \times y^{4} \times y^{2}}$
Simplify multiplication: Simplify the multiplication inside the square root. $\newline$ $15 \times 20 = 300$ $\newline$ $y^{4} \times y^{2} = y^{4+2} = y^{6}$ $\newline$ So, $\sqrt{15 \times 20 \times y^{4} \times y^{2}} = \sqrt{300y^{6}}$
Factor out perfect squares: Factor out perfect squares from the radicand. $\newline$ $300 = 2 \times 2 \times 3 \times 5 \times 5 = 2^2 \times 3 \times 5^2$ $\newline$ $y^{(6)} = (y^{(3)})^2$ $\newline$ So, $\sqrt{300y^{(6)}} = \sqrt{2^2 \times 3 \times 5^2 \times (y^{(3)})^2}$
Take square root: Take the square root of the perfect squares. $\sqrt{2^2 \cdot 3 \cdot 5^2 \cdot (y^{3})^2} = 2 \cdot 5 \cdot y^{3} \cdot \sqrt{3}$ = $10y^{3} \cdot \sqrt{3}$
Multiply with coefficient: Multiply the result from Step $6$ with the coefficient from Step $2$ . $\newline$ $12 \times (10y^{3} \times \sqrt{3}) = 120y^{3} \times \sqrt{3}$

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