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

sqrt(18x^(7)y^(2))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $\sqrt{18 x^{7} y^{2}}$ $\newline$ 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{18 x^{7} y^{2}}

\newline

Answer:

Factor Perfect Squares: Factor the expression inside the square root to identify perfect squares. $\sqrt{18x^{7}y^{2}}$ can be factored into $\sqrt{2 \times 3^{2} \times x^{6} \times x \times y^{2}}$ .
Separate Perfect Squares: Separate the perfect squares from the non-perfect squares inside the radical. $\newline$ We have $\sqrt{3^2 \times x^6 \times y^2 \times 2 \times x}$ which can be written as $\sqrt{3^2} \times \sqrt{x^6} \times \sqrt{y^2} \times \sqrt{2 \times x}$ .
Simplify Square Roots: Simplify the square roots of the perfect squares. Since $\sqrt{3^2} = 3$ , $\sqrt{x^6} = x^3$ , and $\sqrt{y^2} = y$ , we have $3 \times x^3 \times y \times \sqrt{2 \times x}$ .
Combine Simplified Terms: Combine the simplified terms. $\newline$ The expression simplifies to $3x^3y \cdot \sqrt{2x}$ .
Check Simplified Form: Check if the simplified expression is in its simplest radical form. $\newline$ Since $2x$ does not have any perfect square factors other than $1$ , and $x$ is assumed to be positive, the expression $3x^3y \times \sqrt{2x}$ is indeed in its simplest radical form.

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