Question
Answer
$$\dfrac{3\sqrt{14}}{3\sqrt{23}}=\dfrac{\sqrt{322}}{23}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{14}}{3\sqrt{23}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{14}}{3\sqrt{23}}\frac{\sqrt{23}}{\sqrt{23}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3\sqrt{322}}{69} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{322}}{23}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{23}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 \sqrt{14} } \cdot \sqrt{23} = 3 \sqrt{322} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{23} } \cdot \sqrt{23} = 69 $$ |
| ③ | Divide both numerator and denominator by 3. |
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