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Simplify the, following expression. Assume that all variables are positive.

sqrt(8x^(2)y^(6))

Simplify the, following expression. Assume that all variables are positive. $\newline$ $\sqrt{8 x^{2} y^{6}}$

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Simplify radical expressions with variables

Full solution

Q. Simplify the, following expression. Assume that all variables are positive.

\newline

\sqrt{8 x^{2} y^{6}}

Factor and Express Perfect Squares: First, let's factor $8$ into $2^3$ and express $x^2$ and $y^6$ as perfect squares. $\sqrt{8x^{2}y^{6}} = \sqrt{(2^3)(x^2)(y^6)}$
Rewrite Expression with Square Roots: Now, we can rewrite the expression by taking the square root of each perfect square. $\sqrt{(2^3)(x^2)(y^6)} = \sqrt{2^2 \cdot 2 \cdot x^2 \cdot y^2 \cdot y^2 \cdot y^2}$
Take Square Roots of Perfect Squares: Next, we take the square root of the perfect squares $2^2$ , $x^2$ , and $y^2$ three times. $\sqrt{2^2 \cdot 2 \cdot x^2 \cdot y^2 \cdot y^2 \cdot y^2} = 2 \cdot x \cdot y \cdot y \cdot y \cdot \sqrt{2}$
Combine and Simplify: Finally, we simplify the expression by combining the y terms. $\newline$ $2 \times x \times y \times y \times y \times \sqrt{2} = 2xy^3 \times \sqrt{2}$

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