Answer
$$\frac{4\sqrt{60}}{5\sqrt{42}}=\frac{4\sqrt{70}}{35}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{60}}{5\sqrt{42}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{60}}{5\sqrt{42}}\frac{\sqrt{42}}{\sqrt{42}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24\sqrt{70}}{210} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 24 \sqrt{ 70 } : \color{blue}{ 6 } } { 210 : \color{blue}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4\sqrt{70}}{35}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{42}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{60} } \cdot \sqrt{42} = 24 \sqrt{70} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{42} } \cdot \sqrt{42} = 210 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 6 } $. |
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