Question
Answer
$$\dfrac{3}{\sqrt{4}+7}=\dfrac{1}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{\sqrt{4}+7}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{\sqrt{4}+7}\frac{\sqrt{4}-7}{\sqrt{4}-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6-21}{4-14+14-49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-15}{-45} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{15}{45} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}} \frac{ 15 : \color{orangered}{ 15 } }{ 45 : \color{orangered}{ 15 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{4}-7} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 } \cdot \left( \sqrt{4}-7\right) = \color{blue}{3} \cdot \sqrt{4}+\color{blue}{3} \cdot-7 = \\ = 6-21 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{4} + 7\right) } \cdot \left( \sqrt{4}-7\right) = \color{blue}{ \sqrt{4}} \cdot \sqrt{4}+\color{blue}{ \sqrt{4}} \cdot-7+\color{blue}{7} \cdot \sqrt{4}+\color{blue}{7} \cdot-7 = \\ = 4-14 + 14-49 $$ |
| ③ | Simplify numerator and denominator |
| ④ | cancel two minus signs |
| ⑤ | Divide both the top and bottom numbers by $ \color{orangered}{ 15 } $. |
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