Question
Answer
$$\dfrac{\sqrt{5}}{\sqrt{45}}=\dfrac{1}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{5}}{\sqrt{45}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{5}}{\sqrt{45}}\frac{\sqrt{45}}{\sqrt{45}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15}{45} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 15 : \color{orangered}{ 15 } }{ 45 : \color{orangered}{ 15 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{45}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{5} } \cdot \sqrt{45} = 15 $$ Simplify denominator. $$ \color{blue}{ \sqrt{45} } \cdot \sqrt{45} = 45 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 15 } $. |
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