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Simplify.
Remove all perfect squares from inside the square root.

sqrt(56z^(7))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{56z^{7}}=$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root.

\newline

\sqrt{56z^{7}}=

Factorization and Perfect Squares: Factor $56z^7$ into its prime factors and identify perfect squares. $\newline$ $56$ can be factored into $2 \times 2 \times 2 \times 7$ , and $z^7$ can be written as $z^6 \times z$ , where $z^6$ is a perfect square since $6$ is an even number. $\newline$ So, we have $\sqrt{56z^7} = \sqrt{2 \times 2 \times 2 \times 7 \times z^6 \times z}$ .
Grouping Perfect Squares: Group the perfect squares together inside the square root. $\newline$ We can group the perfect squares as follows: $\sqrt{2^2 \cdot 2 \cdot 7 \cdot z^6 \cdot z} = \sqrt{4 \cdot 2 \cdot 7 \cdot z^6 \cdot z}$ .
Simplifying the Square Root: Simplify the square root of the perfect squares. $\newline$ Since $\sqrt{4} = 2$ and $\sqrt{z^6} = z^3$ , we can take them out of the square root. $\newline$ This gives us: $2 \cdot z^3 \cdot \sqrt{2 \cdot 7 \cdot z} = 2z^3 \cdot \sqrt{14z}$ .

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