Answer
$$\frac{\sqrt{3}-3}{\sqrt{16}}=\frac{\sqrt{3}-3}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{3}-3}{\sqrt{16}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{3}-3}{\sqrt{16}}\frac{\sqrt{16}}{\sqrt{16}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{3}-12}{16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{3}-3}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{16}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{3}-3\right) } \cdot \sqrt{16} = \color{blue}{ \sqrt{3}} \cdot \sqrt{16}\color{blue}{-3} \cdot \sqrt{16} = \\ = 4 \sqrt{3}-12 $$ Simplify denominator. $$ \color{blue}{ \sqrt{16} } \cdot \sqrt{16} = 16 $$ |
| ③ | Divide both numerator and denominator by 4. |
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