Question
Answer
$$\dfrac{\sqrt{405}}{4\sqrt{30}}=\dfrac{3\sqrt{6}}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{405}}{4\sqrt{30}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{405}}{4\sqrt{30}}\frac{\sqrt{30}}{\sqrt{30}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{45\sqrt{6}}{120} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 45 \sqrt{ 6 } : \color{blue}{ 15 } } { 120 : \color{blue}{ 15 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{6}}{8}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{30}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{405} } \cdot \sqrt{30} = 45 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{30} } \cdot \sqrt{30} = 120 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 15 } $. |
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