Question
Answer
$$\dfrac{3\sqrt{5}+\sqrt{20}-\sqrt{60}}{\sqrt{5}}=5-2\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{5}+\sqrt{20}-\sqrt{60}}{\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{5}+\sqrt{20}-\sqrt{60}}{\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15+10-10\sqrt{3}}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{25-10\sqrt{3}}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5-2\sqrt{3}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}5-2\sqrt{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 3 \sqrt{5} + \sqrt{20}- \sqrt{60}\right) } \cdot \sqrt{5} = \color{blue}{ 3 \sqrt{5}} \cdot \sqrt{5}+\color{blue}{ \sqrt{20}} \cdot \sqrt{5}\color{blue}{- \sqrt{60}} \cdot \sqrt{5} = \\ = 15 + 10- 10 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{5} } \cdot \sqrt{5} = 5 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 5. |
| ⑤ | Remove 1 from denominator. |
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