Question
Answer
$$\dfrac{3}{\sqrt{2}^5}=\dfrac{3\sqrt{2}}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{\sqrt{2}^5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{4\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3}{4\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3\sqrt{2}}{8}\end{aligned} $$ | |
| ① | $$ \sqrt{2}^5 =
\left( \sqrt{2} ^2 \right)^{ 2 } \cdot \sqrt{2} =
\lvert 2 \rvert ^{ 2 } \cdot \sqrt{2} =
4\sqrt{2} $$ |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ 3 } \cdot \sqrt{2} = 3 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{2} } \cdot \sqrt{2} = 8 $$ |
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