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

xsqrt(4x^(6)y^(3))
Answer:

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $x \sqrt{4 x^{6} y^{3}}$ $\newline$ Answer:

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Simplify radical expressions with variables II

Full solution

Q. Assuming

x

and

y

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

\newline

x \sqrt{4 x^{6} y^{3}}

\newline

Answer:

Simplify constant term: Simplify the square root of the constant term. $\newline$ The constant term inside the square root is $4$ , which is a perfect square ( $2^2$ ). We can take the square root of $4$ out of the radical. $\newline$ $\sqrt{4} = 2$
Simplify variable term $x^{6}$ : Simplify the square root of the variable term $x^{6}$ . Since $x^{6}$ is a perfect square $(x^{3})^{2}$ , we can take $x^{3}$ out of the radical. $\sqrt{x^{6}} = x^{3}$
Simplify variable term $y^{3}$ : Simplify the square root of the variable term $y^{3}$ . We cannot take the entire $y^{3}$ out of the radical because it is not a perfect square. However, we can separate it into $y^{2} \times y$ , where $y^{2}$ is a perfect square and can be taken out of the radical. $\sqrt{y^{3}} = \sqrt{y^{2} \times y} = y \times \sqrt{y}$
Combine results: Combine the results from steps $1$ , $2$ , and $3$ . We multiply the terms that came out of the radical together with the original $x$ that was outside the radical. $x \times 2 \times x^{3} \times y \times \sqrt{y} = 2x^{4}y \times \sqrt{y}$

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