Question
Answer
$$\dfrac{\sqrt{5}^2+3\sqrt{11}^2}{3\sqrt{11}}=\dfrac{38\sqrt{11}}{33}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{5}^2+3\sqrt{11}^2}{3\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{5}^2+3\cdot11}{3\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{5}^2+33}{3\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5+33}{3\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{38}{3\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{38}{3\sqrt{11}}\frac{\sqrt{11}}{\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{38\sqrt{11}}{33}\end{aligned} $$ | |
| ① | $$ \sqrt{11}^2 =
\sqrt{11} ^2 =
\lvert 11 \rvert =
11 $$ |
| ② | $ 3 \cdot 11 = 33 $ |
| ③ | $$ \sqrt{5}^2 =
\sqrt{5} ^2 =
\lvert 5 \rvert =
5 $$ |
| ④ | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{11}} $$. |
| ⑤ | Multiply in a numerator. $$ \color{blue}{ 38 } \cdot \sqrt{11} = 38 \sqrt{11} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{11} } \cdot \sqrt{11} = 33 $$ |
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