Question
Answer
$$\dfrac{7\cdot2\sqrt{5}}{2\sqrt{5}\cdot2\sqrt{5}}=\dfrac{7\sqrt{5}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7\cdot2\sqrt{5}}{2\sqrt{5}\cdot2\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7\cdot2\sqrt{5}}{2\sqrt{5}\cdot2\sqrt{5}}\frac{\sqrt{25}}{\sqrt{25}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{70\sqrt{5}}{100} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 70 \sqrt{ 5 } : \color{blue}{ 10 } } { 100 : \color{blue}{ 10 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{7\sqrt{5}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{25}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 14 \sqrt{5} } \cdot \sqrt{25} = 70 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{25} } \cdot \sqrt{25} = 100 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 10 } $. |
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