Apply square root property: Apply the square root property to the constant 25 inside the square root. sqrt(25sqrt(x^(8))) = 5sqrt(sqrt(x^(8)))Recognize equivalent expression: Recognize that sqrt(sqrt(x)) is equivalent to the fourth root of x, and apply this to x^(8). 5sqrt(sqrt(x^(8))) = 5sqrt(x^(8/4))Simplify exponent: Simplify the exponent by dividing 8 by 4. 5sqrt(x^(8/4)) = 5sqrt(x^(2))Apply square root: Apply the square root to x^2. 5sqrt(x^(2)) = 5 * xAssume non-negative variable: Since x is a variable, we assume it is non-negative, and thus the square root of x^2 is x. 5 * x = 5x

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$\sqrt{25 \sqrt{x^{8}}}$

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Algebra 2

Simplify radical expressions involving fractions

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\sqrt{25 \sqrt{x^{8}}}

Apply square root property: Apply the square root property to the constant $25$ inside the square root. $\sqrt{25\sqrt{x^{8}}} = 5\sqrt{\sqrt{x^{8}}}$
Recognize equivalent expression: Recognize that $\sqrt{\sqrt{x}}$ is equivalent to the fourth root of $x$ , and apply this to $x^{8}$ . $\newline$ $5\sqrt{\sqrt{x^{8}}} = 5\sqrt{x^{(8/4)}}$
Simplify exponent: Simplify the exponent by dividing $8$ by $4$ . $\newline$ $5\sqrt{x^{(8/4)}} = 5\sqrt{x^{2}}$
Apply square root: Apply the square root to $x^2$ . $\newline$ $5\sqrt{x^{(2)}} = 5 \times x$
Assume non-negative variable: Since $x$ is a variable, we assume it is non-negative, and thus the square root of $x^2$ is $x$ . $\newline$ $5 \times x = 5x$