Question
Answer
$$\dfrac{\sqrt{121}}{\sqrt{125}}=\dfrac{11\sqrt{5}}{25}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{121}}{\sqrt{125}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{121}}{\sqrt{125}}\frac{\sqrt{125}}{\sqrt{125}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{55\sqrt{5}}{125} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 55 \sqrt{ 5 } : \color{blue}{ 5 } } { 125 : \color{blue}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{11\sqrt{5}}{25}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{125}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{121} } \cdot \sqrt{125} = 55 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \sqrt{125} } \cdot \sqrt{125} = 125 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 5 } $. |
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