Pregunta
Rationalize the denominator. If possible, simplify the rationalized expression by dividing the numerator and denominator by the greatest common factor. \( \frac{1}{\sqrt{14}}=\square \) (Type a simplified fraction. Simplify your answer.)
Ask by Howell Sanders. in the United States
Mar 12,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\[
\frac{1}{\sqrt{14}} = \frac{\sqrt{14}}{14}
\]
Solución
Multiply the numerator and the denominator by \(\sqrt{14}\):
\[
\frac{1}{\sqrt{14}} \times \frac{\sqrt{14}}{\sqrt{14}} = \frac{\sqrt{14}}{14}
\]
Since \(\sqrt{14}\) and \(14\) have no common factors (other than 1), the expression is fully simplified.
\[
\frac{1}{\sqrt{14}} = \frac{\sqrt{14}}{14}
\]
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Como
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Extra Insights
To rationalize the denominator of \( \frac{1}{\sqrt{14}} \), you would multiply both the numerator and the denominator by \( \sqrt{14} \). This gives you: \[ \frac{1 \cdot \sqrt{14}}{\sqrt{14} \cdot \sqrt{14}} = \frac{\sqrt{14}}{14}. \] Since there are no common factors between the numerator and the denominator, the expression is already in its simplest form. Therefore, the final answer is: \[ \frac{\sqrt{14}}{14}. \]

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