Question
Answer
$$\dfrac{\sqrt{5}}{\sqrt{49}}+\dfrac{\sqrt{20}}{\sqrt{49}}-2\dfrac{\sqrt{45}}{\sqrt{49}}=\dfrac{-3\sqrt{5}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{5}}{\sqrt{49}}+\frac{\sqrt{20}}{\sqrt{49}}-2\frac{\sqrt{45}}{\sqrt{49}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7\sqrt{5}}{49}+\frac{14\sqrt{5}}{49}-2\frac{21\sqrt{5}}{49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{5}}{7}+\frac{14\sqrt{5}}{49}-2\frac{21\sqrt{5}}{49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{7\sqrt{5}+14\sqrt{5}}{49}-2\frac{21\sqrt{5}}{49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{21\sqrt{5}}{49}-2\frac{21\sqrt{5}}{49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{21\sqrt{5}-42\sqrt{5}}{49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{-21\sqrt{5}}{49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{ -21 \sqrt{ 5 } : \color{blue}{ 7 } } { 49 : \color{blue}{ 7 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{-3\sqrt{5}}{7}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{5} } \cdot \sqrt{49} = 7 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \sqrt{49} } \cdot \sqrt{49} = 49 $$Multiply in a numerator. $$ \color{blue}{ \sqrt{20} } \cdot \sqrt{49} = 14 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \sqrt{49} } \cdot \sqrt{49} = 49 $$Multiply in a numerator. $$ \color{blue}{ \sqrt{45} } \cdot \sqrt{49} = 21 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \sqrt{49} } \cdot \sqrt{49} = 49 $$ |
| ② | Divide both numerator and denominator by 7. |
| ③ | $$ \frac{\sqrt{5}}{7}+\frac{14\sqrt{5}}{49}
= \frac{\sqrt{5}}{7} \cdot \color{blue}{\frac{ 7 }{ 7}} + \frac{14\sqrt{5}}{49} \cdot \color{blue}{\frac{ 1 }{ 1}}
= \frac{7\sqrt{5}+14\sqrt{5}}{49} $$ |
| ④ | Simplify numerator and denominator |
| ⑤ | $$ \frac{21\sqrt{5}}{49}-2\frac{21\sqrt{5}}{49}
= \frac{21\sqrt{5}}{49} \cdot \color{blue}{\frac{ 1 }{ 1}} - \frac{42\sqrt{5}}{49} \cdot \color{blue}{\frac{ 1 }{ 1}}
= \frac{21\sqrt{5}-42\sqrt{5}}{49} $$ |
| ⑥ | Simplify numerator and denominator |
| ⑦ | Divide numerator and denominator by $ \color{blue}{ 7 } $. |
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