Question
Answer
$$\dfrac{\sqrt{78}}{\sqrt{54}}=\dfrac{\sqrt{13}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{78}}{\sqrt{54}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{78}}{\sqrt{54}}\frac{\sqrt{54}}{\sqrt{54}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18\sqrt{13}}{54} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{13}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{54}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{78} } \cdot \sqrt{54} = 18 \sqrt{13} $$ Simplify denominator. $$ \color{blue}{ \sqrt{54} } \cdot \sqrt{54} = 54 $$ |
| ③ | Divide both numerator and denominator by 18. |
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