Question
Answer
$$\dfrac{2\sqrt{22}}{\sqrt{55}}=\dfrac{2\sqrt{10}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{22}}{\sqrt{55}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{22}}{\sqrt{55}}\frac{\sqrt{55}}{\sqrt{55}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{22\sqrt{10}}{55} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 22 \sqrt{ 10 } : \color{blue}{ 11 } } { 55 : \color{blue}{ 11 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{10}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{55}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{22} } \cdot \sqrt{55} = 22 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \sqrt{55} } \cdot \sqrt{55} = 55 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 11 } $. |
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