Question
Answer
$$\dfrac{1}{\sqrt{81}\cdot\sqrt{16}}=\dfrac{1}{36}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{\sqrt{81}\cdot\sqrt{16}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{\sqrt{81}\cdot\sqrt{16}}\frac{\sqrt{1296}}{\sqrt{1296}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{36}{1296} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 36 : \color{orangered}{ 36 } }{ 1296 : \color{orangered}{ 36 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{36}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{1296}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 1 } \cdot \sqrt{1296} = 36 $$ Simplify denominator. $$ \color{blue}{ \sqrt{1296} } \cdot \sqrt{1296} = 1296 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 36 } $. |
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