Question
Answer
$$\dfrac{6\sqrt{2}-\sqrt{15}}{\sqrt{10}}=\dfrac{12\sqrt{5}-5\sqrt{6}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6\sqrt{2}-\sqrt{15}}{\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6\sqrt{2}-\sqrt{15}}{\sqrt{10}}\frac{\sqrt{10}}{\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12\sqrt{5}-5\sqrt{6}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 6 \sqrt{2}- \sqrt{15}\right) } \cdot \sqrt{10} = \color{blue}{ 6 \sqrt{2}} \cdot \sqrt{10}\color{blue}{- \sqrt{15}} \cdot \sqrt{10} = \\ = 12 \sqrt{5}- 5 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \sqrt{10} } \cdot \sqrt{10} = 10 $$ |
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