Question
Answer
$$\dfrac{\sqrt{100}}{\sqrt{121}}=\dfrac{10}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{100}}{\sqrt{121}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{100}}{\sqrt{121}}\frac{\sqrt{121}}{\sqrt{121}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{110}{121} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 110 : \color{orangered}{ 11 } }{ 121 : \color{orangered}{ 11 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{10}{11}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{121}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{100} } \cdot \sqrt{121} = 110 $$ Simplify denominator. $$ \color{blue}{ \sqrt{121} } \cdot \sqrt{121} = 121 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 11 } $. |
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