Question
Rationalize the denominator. \( \sqrt{\frac{13 x}{19 y}} \) \( \sqrt{\frac{13 x}{19 y}}=\square \) (Type an exact answer, using radical as needed.)
Ask by Curry Vaughan. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \sqrt{\frac{13x}{19y}} = \frac{\sqrt{247xy}}{19y} \)
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Beyond the Answer
To rationalize the denominator of the expression \( \sqrt{\frac{13 x}{19 y}} \), we can multiply both the numerator and the denominator by \( \sqrt{19 y} \): \[ \sqrt{\frac{13 x}{19 y}} = \frac{\sqrt{13 x} \cdot \sqrt{19 y}}{\sqrt{19 y} \cdot \sqrt{19 y}} = \frac{\sqrt{13 x \cdot 19 y}}{19 y} \] So the rationalized form is: \[ \frac{\sqrt{247 xy}}{19 y} \] Thus, \( \sqrt{\frac{13 x}{19 y}} = \frac{\sqrt{247 xy}}{19 y} \).
