Question
Answer
$$\dfrac{10}{\sqrt{8}}-\sqrt{10}=\dfrac{5\sqrt{2}-2\sqrt{10}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10}{\sqrt{8}}-\sqrt{10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{20\sqrt{2}}{8}-\sqrt{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{20\sqrt{2}-8\sqrt{10}}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5\sqrt{2}-2\sqrt{10}}{2}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ 10 } \cdot \sqrt{8} = 20 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \sqrt{8} } \cdot \sqrt{8} = 8 $$ |
| ② | $$ \frac{20\sqrt{2}}{8}-\sqrt{10}
= \frac{20\sqrt{2}}{8} \cdot \color{blue}{\frac{ 1 }{ 1}} - \sqrt{10} \cdot \color{blue}{\frac{ 8 }{ 8}}
= \frac{20\sqrt{2}-8\sqrt{10}}{8} $$ |
| ③ | Divide both numerator and denominator by 4. |
This page was created using
Simplify Radical Expression