Question
Answer
$$\dfrac{6\sqrt{18}}{12\sqrt{40}}=\dfrac{3\sqrt{5}}{20}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6\sqrt{18}}{12\sqrt{40}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6\sqrt{18}}{12\sqrt{40}}\frac{\sqrt{40}}{\sqrt{40}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{72\sqrt{5}}{480} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 72 \sqrt{ 5 } : \color{blue}{ 24 } } { 480 : \color{blue}{ 24 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{5}}{20}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{40}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 \sqrt{18} } \cdot \sqrt{40} = 72 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 12 \sqrt{40} } \cdot \sqrt{40} = 480 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 24 } $. |
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