Question
Answer
$$\dfrac{10-\sqrt{50}}{5}=2-\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10-\sqrt{50}}{5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10-5\sqrt{2}}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2-\sqrt{2}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2-\sqrt{2}\end{aligned} $$ | |
| ① | $$ - \sqrt{50} =
- \sqrt{ 5 ^2 \cdot 2 } =
- \sqrt{ 5 ^2 } \, \sqrt{ 2 } =
- 5 \sqrt{ 2 }$$ |
| ② | Divide both numerator and denominator by 5. |
| ③ | Remove 1 from denominator. |
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