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Assuming
x and
y are both positive, write the following expression in simplest radical form.

3sqrt(28x^(2)y^(3))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $3 \sqrt{28 x^{2} y^{3}}$ $\newline$ Answer:

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Simplify the product of two radical expressions having same variable

Full solution

Q. Assuming

x

and

y

are both positive, write the following expression in simplest radical form.

\newline

3 \sqrt{28 x^{2} y^{3}}

\newline

Answer:

Simplify Radicand: Simplify the radicand (the number inside the radical). We have $28x^2y^3$ under the square root. The number $28$ can be factored into $4$ and $7$ , where $4$ is a perfect square. Also, $x^2$ is a perfect square, and $y^3$ can be split into $y^2$ (a perfect square) and $y$ . $3\sqrt{28x^2y^3} = 3\sqrt{4\cdot7\cdot x^2\cdot y^2\cdot y}$
Take Out Perfect Squares: Take out the perfect squares from under the radical. $\newline$ Since $4$ , $x^2$ , and $y^2$ are perfect squares, we can take their square roots out of the radical. $\newline$ $3\sqrt{4\cdot7\cdot x^2\cdot y^2\cdot y} = 3\cdot2\cdot x\cdot y\cdot\sqrt{7y}$ $\newline$ $3\sqrt{28x^2y^3} = 6xy\cdot\sqrt{7y}$
Combine Constants and Variables: Combine the constants and variables outside the radical. We multiply the constants and variables that are outside the radical to simplify the expression. $6xy\sqrt{7y}$ This is already simplified, and there are no further simplifications needed.

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