Answer
$$\frac{\sqrt{32}}{\sqrt{256}}=\frac{\sqrt{2}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{32}}{\sqrt{256}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{32}}{\sqrt{256}}\frac{\sqrt{256}}{\sqrt{256}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{64\sqrt{2}}{256} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{256}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{32} } \cdot \sqrt{256} = 64 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \sqrt{256} } \cdot \sqrt{256} = 256 $$ |
| ③ | Divide both numerator and denominator by 64. |
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