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

3x^(2)y^(2)sqrt(28x^(5)y^(2))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $3 x^{2} y^{2} \sqrt{28 x^{5} y^{2}}$ $\newline$ Answer:

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Simplify radical expressions with root inside the root

Full solution

Q. Assuming

x

and

y

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

\newline

3 x^{2} y^{2} \sqrt{28 x^{5} y^{2}}

\newline

Answer:

Write Expression and Identify Simplification: Write the given expression and identify the parts that can be simplified. $\newline$ The given expression is $3x^{2}y^{2}\sqrt{28x^{5}y^{2}}$ . We can simplify the square root by factoring out perfect squares.
Factor Expression to Identify Perfect Squares: Factor the expression inside the square root to identify perfect squares. $\sqrt{28x^{5}y^{2}}$ can be written as $\sqrt{4 \times 7 \times x^{4} \times x \times y^{2}}$ . We notice that $4$ , $x^{4}$ , and $y^{2}$ are perfect squares.
Take Perfect Squares out of Square Root: Take the perfect squares out of the square root. $\newline$ $\sqrt{4 \times 7 \times x^{4} \times x \times y^{2}} = \sqrt{4} \times \sqrt{x^{4}} \times \sqrt{y^{2}} \times \sqrt{7x}$ $\newline$ $= 2 \times x^{2} \times y \times \sqrt{7x}$ .
Multiply Simplified Square Root: Multiply the simplified square root with the rest of the given expression. $\newline$ Now we have $3x^{2}y^{2} \times (2 \times x^{2} \times y \times \sqrt{7x})$ $\newline$ = $3 \times 2 \times x^{2} \times x^{2} \times y^{2} \times y \times \sqrt{7x}$ $\newline$ = $6 \times x^{4} \times y^{3} \times \sqrt{7x}$ .
Write Final Simplified Expression: Write the final simplified expression. $\newline$ The expression $6 \times x^{4} \times y^{3} \times \sqrt{7x}$ is the simplest radical form of the given expression.

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