Simplify. Remove all perfect squares from inside the square roots. Assume y and z are positive. sqrt(75 yz^(2))=

Factor out perfect squares: Identify and factor out the perfect squares from inside the square root. sqrt(75 yz^(2)) can be broken down into sqrt(25 * 3 * y * z^2). Since 25 and z^2 are perfect squares, we can take them out of the square root.Simplify square root: Simplify the square root by taking out the perfect squares. sqrt(25 * 3 * y * z^2) = sqrt(25) * sqrt(3) * sqrt(y) * sqrt(z^2) = 5 * sqrt(3) * sqrt(y) * zCombine terms for final form: Combine the terms outside the square root to get the final simplified form. 5 * sqrt(3) * sqrt(y) * z = 5z * sqrt(3y)

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Simplify.
Remove all perfect squares from inside the square roots. Assume
y and
z are positive.

sqrt(75 yz^(2))=

Simplify. $\newline$ Remove all perfect squares from inside the square roots. Assume $\newline$ $y$ and $\newline$ $z$ are positive. $\newline$ $\sqrt{75 yz^{2}}$ =

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Math Problems

Algebra 1

Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square roots. Assume

\newline

y

and

\newline

z

are positive.

\newline

\sqrt{75 yz^{2}}

Factor out perfect squares: Identify and factor out the perfect squares from inside the square root. $\sqrt{75 yz^{2}}$ can be broken down into $\sqrt{25 \times 3 \times y \times z^2}$ . Since $25$ and $z^2$ are perfect squares, we can take them out of the square root.
Simplify square root: Simplify the square root by taking out the perfect squares. $\sqrt{25 \times 3 \times y \times z^2} = \sqrt{25} \times \sqrt{3} \times \sqrt{y} \times \sqrt{z^2}$ = $5 \times \sqrt{3} \times \sqrt{y} \times z$
Combine terms for final form: Combine the terms outside the square root to get the final simplified form. $\newline$ $5 \cdot \sqrt{3} \cdot \sqrt{y} \cdot z = 5z \cdot \sqrt{3y}$