1Cademy - Simplifying Variable Roots with Odd Indices

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Properties of $\sqrt[n]{a}$

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Simplifying Variable Roots with Odd Indices

When simplifying a radical expression where the index $n$ is odd, the property $\sqrt[n]{a^n} = a$ is applied. Unlike roots with even indices, odd-indexed roots do not require absolute value signs because odd powers preserve the original sign of the base. To simplify an odd root of a variable expression, rewrite the radicand as a perfect $n$ th power. For example, to simplify $\sqrt[3]{y^{18}}$ , recognize that $(y^6)^3 = y^{18}$ . Applying the property yields $\sqrt[3]{(y^6)^3} = y^6$ . The result retains its sign automatically without the need for absolute value bars.