Pregunta
Simplify. \[ \sqrt{\frac{9}{81}} \] Be sure to write your answer in simplest form.
Ask by Bowers Sanders. in the United States
Jan 30,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\(\frac{1}{3}\)
Solución
To simplify the expression \(\sqrt{\frac{9}{81}}\), follow these steps:
1. **Simplify the Fraction Inside the Square Root:**
\[
\frac{9}{81} = \frac{1}{9}
\]
(Since both the numerator and the denominator can be divided by 9.)
2. **Take the Square Root:**
\[
\sqrt{\frac{1}{9}} = \frac{\sqrt{1}}{\sqrt{9}} = \frac{1}{3}
\]
(Because \(\sqrt{1} = 1\) and \(\sqrt{9} = 3\).)
So, the expression \(\sqrt{\frac{9}{81}}\) simplifies to:
\[
\frac{1}{3}
\]
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Simplifique esta solución Extra Insights
To simplify \(\sqrt{\frac{9}{81}}\), we first recognize that both the numerator and the denominator can be simplified separately. We know that \(9\) is a perfect square and \(81\) is also a perfect square. Calculating the square roots, we get: \[ \sqrt{9} = 3 \quad \text{and} \quad \sqrt{81} = 9. \] Now we can simplify the expression: \[ \sqrt{\frac{9}{81}} = \frac{\sqrt{9}}{\sqrt{81}} = \frac{3}{9}. \] Next, we can simplify this fraction: \[ \frac{3}{9} = \frac{1}{3}. \] Thus, the answer in simplest form is: \[ \frac{1}{3}. \]
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