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Express the radical in simplified form. Assume that all variables represent positive real numbers. \( \sqrt{\frac{y^{5}}{25}} \)

Ask by Christensen Bernard. in the United States
Feb 22,2025

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The simplified form of \( \sqrt{\frac{y^{5}}{25}} \) is \( \frac{y^{2}\sqrt{y}}{5} \).

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To simplify the expression \( \sqrt{\frac{y^{5}}{25}} \), we can separate the square root of the numerator and the denominator. This gives us: \[ \sqrt{\frac{y^{5}}{25}} = \frac{\sqrt{y^{5}}}{\sqrt{25}} \] Since \( \sqrt{25} = 5 \) and \( \sqrt{y^{5}} = y^{\frac{5}{2}} = y^{2} \sqrt{y} \), we can rewrite the expression as: \[ \frac{y^{2} \sqrt{y}}{5} = \frac{y^{2} \sqrt{y}}{5} \] Thus, the simplified form is: \[ \frac{y^{2} \sqrt{y}}{5} \]

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