Answer
$$\frac{10\sqrt{7}}{\sqrt{45}}=\frac{2\sqrt{35}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10\sqrt{7}}{\sqrt{45}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10\sqrt{7}}{\sqrt{45}}\frac{\sqrt{45}}{\sqrt{45}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30\sqrt{35}}{45} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 30 \sqrt{ 35 } : \color{blue}{ 15 } } { 45 : \color{blue}{ 15 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{35}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{45}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 10 \sqrt{7} } \cdot \sqrt{45} = 30 \sqrt{35} $$ Simplify denominator. $$ \color{blue}{ \sqrt{45} } \cdot \sqrt{45} = 45 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 15 } $. |
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