Question
Answer
$$\dfrac{\sqrt{5}}{\sqrt{3}}+4\sqrt{7}=\dfrac{\sqrt{15}+12\sqrt{7}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{5}}{\sqrt{3}}+4\sqrt{7}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{15}}{3}+4\sqrt{7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{15}+12\sqrt{7}}{3}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{5} } \cdot \sqrt{3} = \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \sqrt{3} } \cdot \sqrt{3} = 3 $$ |
| ② | $$ \frac{\sqrt{15}}{3}+4\sqrt{7}
= \frac{\sqrt{15}}{3} \cdot \color{blue}{\frac{ 1 }{ 1}} + 4\sqrt{7} \cdot \color{blue}{\frac{ 3 }{ 3}}
= \frac{\sqrt{15}+12\sqrt{7}}{3} $$ |
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