Question
Answer
$$\dfrac{5\sqrt{2}}{\sqrt{66}}=\dfrac{5\sqrt{33}}{33}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5\sqrt{2}}{\sqrt{66}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5\sqrt{2}}{\sqrt{66}}\frac{\sqrt{66}}{\sqrt{66}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{33}}{66} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 10 \sqrt{ 33 } : \color{blue}{ 2 } } { 66 : \color{blue}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{33}}{33}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{66}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 \sqrt{2} } \cdot \sqrt{66} = 10 \sqrt{33} $$ Simplify denominator. $$ \color{blue}{ \sqrt{66} } \cdot \sqrt{66} = 66 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 2 } $. |
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