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

sqrt(52x^(4))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{52x^{4}}=$

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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{52x^{4}}=

Factorize and express $x^4$ : Factorize the number $52$ and express $x^4$ as a square of squares. $\newline$ $52$ can be factorized into $2 \times 2 \times 13$ , which is $4 \times 13$ . Since $x^4$ is $(x^2)^2$ , it is already a perfect square.
Rewrite with factorized form: Rewrite the square root expression with the factorized form. $\sqrt{52x^{4}}$ becomes $\sqrt{4 \times 13 \times (x^2)^2}$ .
Simplify the square root: Simplify the square root by taking out the perfect squares. $\sqrt{4 \cdot 13 \cdot (x^2)^2}$ becomes $2 \cdot x^2 \cdot \sqrt{13}$ because $\sqrt{4}$ is $2$ and $\sqrt{(x^2)^2}$ is $x^2$ .
Write the final expression: Write the final simplified expression. $\newline$ The final simplified expression is $2x^2 \cdot \sqrt{13}$ .

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