Question
Answer
$$\dfrac{5}{3\sqrt{2}+4}=\dfrac{15\sqrt{2}-20}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{3\sqrt{2}+4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{3\sqrt{2}+4}\frac{3\sqrt{2}-4}{3\sqrt{2}-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15\sqrt{2}-20}{18-12\sqrt{2}+12\sqrt{2}-16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15\sqrt{2}-20}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3 \sqrt{2}-4} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( 3 \sqrt{2}-4\right) = \color{blue}{5} \cdot 3 \sqrt{2}+\color{blue}{5} \cdot-4 = \\ = 15 \sqrt{2}-20 $$ Simplify denominator. $$ \color{blue}{ \left( 3 \sqrt{2} + 4\right) } \cdot \left( 3 \sqrt{2}-4\right) = \color{blue}{ 3 \sqrt{2}} \cdot 3 \sqrt{2}+\color{blue}{ 3 \sqrt{2}} \cdot-4+\color{blue}{4} \cdot 3 \sqrt{2}+\color{blue}{4} \cdot-4 = \\ = 18- 12 \sqrt{2} + 12 \sqrt{2}-16 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator