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Simplify.
Remove all perfect squares from inside the square root. Assume
z is positive.

sqrt(72z^(5))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $\newline$ $z$ is positive. $\newline$ $\sqrt{72z^{5}}$ =

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root. Assume

\newline

z

is positive.

\newline

\sqrt{72z^{5}}

=

Factorizing $72$ and expressing $z^5$ : Factor the number $72$ and express $z^5$ in terms of squares. $\newline$ $72$ can be factored into $2 \times 2 \times 2 \times 3 \times 3$ , which is $2^3 \times 3^2$ . The expression $z^5$ can be written as $z^4 \times z$ , where $z^4$ is a perfect square.
Rewriting the square root expression: Rewrite the square root expression using the factors from Step $1$ . $\newline$ $\sqrt{72z^5}$ becomes $\sqrt{2^3 \cdot 3^2 \cdot z^4 \cdot z}$ .
Separating perfect squares: Separate the perfect squares from the non-perfect squares inside the square root. $\newline$ This gives us $\sqrt{2^2 \cdot 3^2 \cdot z^4} \cdot \sqrt{2 \cdot z}$ .
Simplifying the perfect squares: Simplify the square root of the perfect squares. $\newline$ Since $\sqrt{2^2}$ is $2$ , $\sqrt{3^2}$ is $3$ , and $\sqrt{z^4}$ is $z^2$ , we get $2 \times 3 \times z^2 \times \sqrt{2z}$ .
Multiplying outside the square root: Multiply the numbers and variables outside the square root. $\newline$ This results in $6z^2 \cdot \sqrt{2z}$ .
Writing the final simplified expression: Write the final simplified expression. $\newline$ The final simplified expression is $6z^2 \cdot \sqrt{2z}$ .

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