Answer
$$\frac{10-\sqrt{18}}{\sqrt{2}}=5\sqrt{2}-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10-\sqrt{18}}{\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10-\sqrt{18}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{2}-6}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5\sqrt{2}-3}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5\sqrt{2}-3\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 10- \sqrt{18}\right) } \cdot \sqrt{2} = \color{blue}{10} \cdot \sqrt{2}\color{blue}{- \sqrt{18}} \cdot \sqrt{2} = \\ = 10 \sqrt{2}-6 $$ Simplify denominator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{2} = 2 $$ |
| ③ | Divide both numerator and denominator by 2. |
| ④ | Remove 1 from denominator. |
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