Question
Answer
$$\dfrac{6+\sqrt{40}}{\sqrt{10}}=\dfrac{3\sqrt{10}+10}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6+\sqrt{40}}{\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6+\sqrt{40}}{\sqrt{10}}\frac{\sqrt{10}}{\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{10}+20}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3\sqrt{10}+10}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 6 + \sqrt{40}\right) } \cdot \sqrt{10} = \color{blue}{6} \cdot \sqrt{10}+\color{blue}{ \sqrt{40}} \cdot \sqrt{10} = \\ = 6 \sqrt{10} + 20 $$ Simplify denominator. $$ \color{blue}{ \sqrt{10} } \cdot \sqrt{10} = 10 $$ |
| ③ | Divide both numerator and denominator by 2. |
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