Answer
$$\frac{\sqrt{150}}{\sqrt{38}}=\frac{5\sqrt{57}}{19}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{150}}{\sqrt{38}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{150}}{\sqrt{38}}\frac{\sqrt{38}}{\sqrt{38}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{57}}{38} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 10 \sqrt{ 57 } : \color{blue}{ 2 } } { 38 : \color{blue}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{57}}{19}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{38}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{150} } \cdot \sqrt{38} = 10 \sqrt{57} $$ Simplify denominator. $$ \color{blue}{ \sqrt{38} } \cdot \sqrt{38} = 38 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 2 } $. |
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