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

x^(2)y^(2)sqrt(24x^(4)y^(2))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $x^{2} y^{2} \sqrt{24 x^{4} y^{2}}$ $\newline$ 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

x^{2} y^{2} \sqrt{24 x^{4} y^{2}}

\newline

Answer:

Express in Exponential Form: First, let's express the square root in exponential form and then combine the exponents with the same base. $\newline$ $x^{2}y^{2}\sqrt{24x^{4}y^{2}}$ $\newline$ = $x^{2}y^{2}(24x^{4}y^{2})^{\frac{1}{2}}$
Apply Power Rules: Now, apply the power to a product rule and the power to a power rule to the expression inside the square root. $\newline$ $(24x^{4}y^{2})^{\frac{1}{2}}$ $\newline$ = $24^{\frac{1}{2}}$ * $(x^{4})^{\frac{1}{2}}$ * $(y^{2})^{\frac{1}{2}}$ $\newline$ = $2$ * $\sqrt{6}$ * $x^{2}$ * $y$
Multiply Inside and Outside: Next, multiply the expression obtained from the square root with the terms outside the square root. $\newline$ $x^{2}y^{2} \times (2 \times \sqrt{6} \times x^{2} \times y)$ $\newline$ = $2 \times x^{2} \times x^{2} \times y^{2} \times y \times \sqrt{6}$
Combine Like Terms: Combine the like terms by adding the exponents for the bases $x$ and $y$ . $\newline$ = $2 \times x^{(2+2)} \times y^{(2+1)} \times \sqrt{6}$ $\newline$ = $2 \times x^{4} \times y^{3} \times \sqrt{6}$
Simplify Radical Form: The expression is now simplified to its simplest radical form.

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