Question
Answer
$$\dfrac{3\sqrt{26}}{3\sqrt{52}}=\dfrac{\sqrt{2}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{26}}{3\sqrt{52}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{26}}{3\sqrt{52}}\frac{\sqrt{52}}{\sqrt{52}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{78\sqrt{2}}{156} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{52}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 \sqrt{26} } \cdot \sqrt{52} = 78 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{52} } \cdot \sqrt{52} = 156 $$ |
| ③ | Divide both numerator and denominator by 78. |
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