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

sqrt(25x^(4)y^(7))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $\sqrt{25 x^{4} y^{7}}$ $\newline$ Answer:

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Simplify radical expressions with variables

Full solution

Q. Assuming

x

and

y

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

\newline

\sqrt{25 x^{4} y^{7}}

\newline

Answer:

Identify Perfect Squares: Identify the perfect squares within the radical. The expression inside the square root is $25x^{4}y^{7}$ . We can identify the perfect squares as $25$ , $x^{4}$ , and $y^{6}$ because $25$ is a perfect square ( $5^{2}$ ), $x^{4}$ is a perfect square ( $(x^{2})^{2}$ ), and $y^{6}$ is a perfect square ( $(y^{3})^{2}$ ). The $25$ $0$ can be written as $25$ $1$ to separate the perfect square from the remaining factor.
Rewrite Expression: Rewrite the expression separating the perfect squares. $\newline$ We can rewrite $\sqrt{25x^{4}y^{7}}$ as $\sqrt{25}$ * $\sqrt{x^{4}}$ * $\sqrt{y^{6}}$ * $\sqrt{y}$ .
Simplify Square Roots: Simplify the square roots of the perfect squares. Since $\sqrt{25} = 5$ , $\sqrt{x^{4}} = x^2$ , and $\sqrt{y^{6}} = y^3$ , we can simplify the expression to $5 \times x^2 \times y^3 \times \sqrt{y}$ .
Combine Simplified Terms: Combine the simplified terms. $\newline$ The final simplified expression is $5x^2y^3\sqrt{y}$ .

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