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

sqrt(20x^(8))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. Assume $\newline$ $x$ is positive. $\newline$ $\sqrt{20x^{8}}=$

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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

x

is positive.

\newline

\sqrt{20x^{8}}=

Factor the expression: Factor the expression inside the square root to identify perfect squares. $\newline$ The expression inside the square root is $20x^8$ . We can factor $20$ as $4 \times 5$ , and $x^8$ is a perfect square since $8$ is an even number. $\newline$ So, $20x^8$ can be written as $(4 \times 5 \times x^8)$ .
Recognize and rewrite the square root: Recognize the perfect squares and rewrite the square root. $\newline$ The number $4$ is a perfect square ( $2^2$ ), and $x^8$ is a perfect square ( $x^4$ )^ $2$ . Therefore, we can rewrite the square root as: $\newline$ $\sqrt{20x^8} = \sqrt{4 \cdot 5 \cdot x^8} = \sqrt{2^2 \cdot 5 \cdot (x^4)^2}$ .
Simplify the square root: Simplify the square root by taking out the perfect squares. $\newline$ Since we can take the square root of any perfect square, we get: $\newline$ $\sqrt{2^2 \cdot 5 \cdot (x^4)^2} = 2 \cdot x^4 \cdot \sqrt{5}$ .
Write the final expression: Write the final simplified expression. $\newline$ The final simplified expression is $2x^4 \cdot \sqrt{5}$ .

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