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

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Find trigonometric ratios using reference angles

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Q. Simplify. Remove all perfect squares from inside the square roots. Assume

y

and

z

are positive.

\newline

\sqrt{75 yz^{2}}

=

Factorize $75$ : First, we need to factor $75$ into its prime factors to identify any perfect squares. The prime factorization of $75$ is $3 \times 5^2$ . Since $5^2$ is a perfect square, we can take it out of the square root.
Separate perfect squares: Next, we look at the variables $y$ and $z^2$ . Since $y$ is not raised to an even power, it remains inside the square root. However, $z^2$ is a perfect square, so we can take $z$ out of the square root.
Rewrite square root: Now, we rewrite the square root by separating the perfect squares from the non-perfect squares. We have $\sqrt{75 * y * z^2} = \sqrt{3 * 5^2 * y * z^2}$ .
Simplify square root: We can now simplify the square root by taking out the perfect squares. This gives us $\sqrt{3 \times 5^2 \times y \times z^2} = 5z \times \sqrt{3y}$ .
Final simplified form: The final simplified form is $5z \times \sqrt{3y}$ , with all perfect squares removed from inside the square root.

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