Question
Answer
$$\dfrac{6\sqrt{17}}{3\sqrt{34}}=\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6\sqrt{17}}{3\sqrt{34}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6\sqrt{17}}{3\sqrt{34}}\frac{\sqrt{34}}{\sqrt{34}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{102\sqrt{2}}{102} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }\sqrt{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{34}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 \sqrt{17} } \cdot \sqrt{34} = 102 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{34} } \cdot \sqrt{34} = 102 $$ |
| ③ | Divide both numerator and denominator by 102. |
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