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

sqrt(200y^(4))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $\newline$ $y$ is positive. $\newline$ $\sqrt{200y^{4}} =$

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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

y

is positive.

\newline

\sqrt{200y^{4}} =

Factorize and Separate Powers: Break down the number $200$ into its prime factors and separate the powers of $y$ . $200$ can be factored into $2 \times 100$ , and $100$ is a perfect square ( $10^2$ ). The variable $y^4$ is also a perfect square since $(y^2)^2 = y^4$ . $\sqrt{200y^{4}} = \sqrt{2 \times 100 \times y^{4}}$
Simplify Square Root: Simplify the square root by taking out the perfect squares. $\newline$ The square root of $100$ is $10$ , and the square root of $y^4$ is $y^2$ . $\newline$ $\sqrt{200y^{4}} = \sqrt{2} \times \sqrt{100} \times \sqrt{y^{4}} = \sqrt{2} \times 10 \times y^2$
Combine Simplified Terms: Combine the simplified terms outside the square root. Since $\sqrt{2}$ remains under the square root and $10 \cdot y^2$ are outside, we combine them to get the final simplified expression. $\sqrt{200y^{4}} = 10y^2 \cdot \sqrt{2}$

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