Question
Answer
$$\dfrac{3\sqrt{10}}{5+4\sqrt{2}}=\dfrac{-15\sqrt{10}+24\sqrt{5}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{10}}{5+4\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{10}}{5+4\sqrt{2}}\frac{5-4\sqrt{2}}{5-4\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15\sqrt{10}-24\sqrt{5}}{25-20\sqrt{2}+20\sqrt{2}-32} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15\sqrt{10}-24\sqrt{5}}{-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-15\sqrt{10}+24\sqrt{5}}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5- 4 \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 \sqrt{10} } \cdot \left( 5- 4 \sqrt{2}\right) = \color{blue}{ 3 \sqrt{10}} \cdot5+\color{blue}{ 3 \sqrt{10}} \cdot- 4 \sqrt{2} = \\ = 15 \sqrt{10}- 24 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( 5 + 4 \sqrt{2}\right) } \cdot \left( 5- 4 \sqrt{2}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot- 4 \sqrt{2}+\color{blue}{ 4 \sqrt{2}} \cdot5+\color{blue}{ 4 \sqrt{2}} \cdot- 4 \sqrt{2} = \\ = 25- 20 \sqrt{2} + 20 \sqrt{2}-32 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator