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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 $x$ is positive. $\newline$ $\sqrt{20 x^{8}}=$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root. Assume

x

is positive.

\newline

\sqrt{20 x^{8}}=

Factor Perfect Squares: Factor the expression inside the square root to identify perfect squares. We need to factor $20x^8$ to find perfect squares that can be taken out of the square root. $20x^8 = 2^2 \times 5 \times x^8$
Identify & Take Out: Identify and take out the perfect squares from under the square root. The perfect squares in the factorization are $2^2$ and $x^8$ (since $x^8 = (x^4)^2$ ). $\sqrt{20x^8} = \sqrt{2^2 \times 5 \times x^8} = \sqrt{2^2} \times \sqrt{x^8} \times \sqrt{5}$
Simplify Square Roots: Simplify the square roots of the perfect squares. $\sqrt{2^2} = 2$ and $\sqrt{x^8} = x^4$ So, $\sqrt{20x^8} = 2 \times x^4 \times \sqrt{5}$
Write Final Expression: Write the final simplified expression. $\newline$ The expression simplified is $2x^4 \sqrt{5}$ .

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