Question
Answer
$$\dfrac{665}{7\sqrt{45}}=\dfrac{19\sqrt{5}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{665}{7\sqrt{45}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{665}{7\sqrt{45}}\frac{\sqrt{45}}{\sqrt{45}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1995\sqrt{5}}{315} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 1995 \sqrt{ 5 } : \color{blue}{ 105 } } { 315 : \color{blue}{ 105 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{19\sqrt{5}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{45}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 665 } \cdot \sqrt{45} = 1995 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 7 \sqrt{45} } \cdot \sqrt{45} = 315 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 105 } $. |
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