Simplify. sqrt(11x^(2))

Identify Expression: Identify the expression to be simplified. The expression is √(11x^2).Recognize Inverse Operations: Recognize that the square root and the square power are inverse operations. The square root of x squared is x, as long as x is non-negative. This is because √(x^2) = |x|.Apply Square Root Separately: Apply the square root to both 11 and x^2 separately. Since 11 is not a perfect square, it remains under the square root. However, x^2 is a perfect square, so the square root of x^2 is |x|. √(11x^2) = √(11) * √(x^2) = √(11) * |x|.Determine Final Form: Determine the final simplified form. The simplified form is √(11) * |x|. Since we do not know if x is positive or negative, we keep the absolute value to ensure the result is non-negative, as required by the definition of the square root function.

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Simplify. $\newline$ $\sqrt{11x^{2}}$

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Algebra 2

Evaluate rational exponents

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Q. Simplify.

\newline

\sqrt{11x^{2}}

Identify Expression: Identify the expression to be simplified. $\newline$ The expression is $\sqrt{11x^2}$ .
Recognize Inverse Operations: Recognize that the square root and the square power are inverse operations. $\newline$ The square root of $x^2$ is $x$ , as long as $x$ is non-negative. This is because $\sqrt{x^2} = |x|$ .
Apply Square Root Separately: Apply the square root to both $11$ and $x^2$ separately. $\newline$ Since $11$ is not a perfect square, it remains under the square root. However, $x^2$ is a perfect square, so the square root of $x^2$ is $|x|$ . $\newline$ $\sqrt{11x^2} = \sqrt{11} \times \sqrt{x^2} = \sqrt{11} \times |x|$ .
Determine Final Form: Determine the final simplified form. $\newline$ The simplified form is $\sqrt{11} \cdot |x|$ . Since we do not know if $x$ is positive or negative, we keep the absolute value to ensure the result is non-negative, as required by the definition of the square root function.