Answer
$$\frac{10\sqrt{12}}{\sqrt{42}}=\frac{10\sqrt{14}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10\sqrt{12}}{\sqrt{42}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10\sqrt{12}}{\sqrt{42}}\frac{\sqrt{42}}{\sqrt{42}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{60\sqrt{14}}{42} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 60 \sqrt{ 14 } : \color{blue}{ 6 } } { 42 : \color{blue}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{10\sqrt{14}}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{42}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 10 \sqrt{12} } \cdot \sqrt{42} = 60 \sqrt{14} $$ Simplify denominator. $$ \color{blue}{ \sqrt{42} } \cdot \sqrt{42} = 42 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 6 } $. |
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