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

2y^(2)sqrt(18x^(6)y^(4))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $2 y^{2} \sqrt{18 x^{6} y^{4}}$ $\newline$ Answer:

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Evaluate rational expressions

Full solution

Q. Assuming

x

and

y

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

\newline

2 y^{2} \sqrt{18 x^{6} y^{4}}

\newline

Answer:

Factor and Identify Perfect Squares: First, let's factor the radicand (the number inside the square root) to see if any factors are perfect squares. $\sqrt{18x^{6}y^{4}}$ can be broken down into $\sqrt{2 \times 9 \times x^{6} \times y^{4}}$ . We know that $9$ is a perfect square, $x^{6}$ is a perfect square since $6$ is an even number, and $y^{4}$ is a perfect square since $4$ is an even number.
Take Square Roots of Perfect Squares: Now, let's take the square root of the perfect squares. $\sqrt{9} = 3$ , $\sqrt{x^{6}} = x^{3}$ , and $\sqrt{y^{4}} = y^{2}$ . So, $\sqrt{18x^{6}y^{4}}$ simplifies to $3x^{3}y^{2} \sqrt{2}$ .
Multiply Outside Term: Next, we multiply the outside term $2y^{2}$ by the simplified square root term. $\newline$ $2y^{2} \times 3x^{3}y^{2} \times \sqrt{2} = 6x^{3}y^{4} \times \sqrt{2}.$
Simplify to Simplest Form: Finally, we have simplified the expression to its simplest radical form. $\newline$ The expression $2y^{2}\sqrt{18x^{6}y^{4}}$ simplifies to $6x^{3}y^{4} \sqrt{2}$ .

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