Question
Answer
$$\dfrac{23\sqrt{23}-23\sqrt{2}}{5\sqrt{46}}=\dfrac{23\sqrt{2}-2\sqrt{23}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{23\sqrt{23}-23\sqrt{2}}{5\sqrt{46}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{23\sqrt{23}-23\sqrt{2}}{5\sqrt{46}}\frac{\sqrt{46}}{\sqrt{46}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{529\sqrt{2}-46\sqrt{23}}{230} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{23\sqrt{2}-2\sqrt{23}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{46}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 23 \sqrt{23}- 23 \sqrt{2}\right) } \cdot \sqrt{46} = \color{blue}{ 23 \sqrt{23}} \cdot \sqrt{46}\color{blue}{- 23 \sqrt{2}} \cdot \sqrt{46} = \\ = 529 \sqrt{2}- 46 \sqrt{23} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{46} } \cdot \sqrt{46} = 230 $$ |
| ③ | Divide both numerator and denominator by 23. |
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