Question
Answer
$$\dfrac{3\sqrt{5}+7\sqrt{3}}{5\sqrt{24}}=\dfrac{\sqrt{30}+7\sqrt{2}}{20}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{5}+7\sqrt{3}}{5\sqrt{24}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{5}+7\sqrt{3}}{5\sqrt{24}}\frac{\sqrt{24}}{\sqrt{24}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{30}+42\sqrt{2}}{120} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{30}+7\sqrt{2}}{20}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{24}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 3 \sqrt{5} + 7 \sqrt{3}\right) } \cdot \sqrt{24} = \color{blue}{ 3 \sqrt{5}} \cdot \sqrt{24}+\color{blue}{ 7 \sqrt{3}} \cdot \sqrt{24} = \\ = 6 \sqrt{30} + 42 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{24} } \cdot \sqrt{24} = 120 $$ |
| ③ | Divide both numerator and denominator by 6. |
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