Question
Answer
$$\dfrac{5\sqrt{7}-\sqrt{7}}{\sqrt{21}}=\dfrac{4\sqrt{3}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5\sqrt{7}-\sqrt{7}}{\sqrt{21}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{7}}{\sqrt{21}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{7}}{\sqrt{21}}\frac{\sqrt{21}}{\sqrt{21}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{28\sqrt{3}}{21} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{ 28 \sqrt{ 3 } : \color{blue}{ 7 } } { 21 : \color{blue}{ 7 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4\sqrt{3}}{3}\end{aligned} $$ | |
| ① | Simplify numerator and denominator |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{21}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{7} } \cdot \sqrt{21} = 28 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{21} } \cdot \sqrt{21} = 21 $$ |
| ④ | Divide numerator and denominator by $ \color{blue}{ 7 } $. |
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