Question
Answer
$$\dfrac{5\sqrt{3}-2\sqrt{18}}{3\sqrt{14}+\sqrt{6}}=\dfrac{5\sqrt{42}-5\sqrt{2}-12\sqrt{7}+4\sqrt{3}}{40}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5\sqrt{3}-2\sqrt{18}}{3\sqrt{14}+\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5\sqrt{3}-2\sqrt{18}}{3\sqrt{14}+\sqrt{6}}\frac{3\sqrt{14}-\sqrt{6}}{3\sqrt{14}-\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15\sqrt{42}-15\sqrt{2}-36\sqrt{7}+12\sqrt{3}}{126-6\sqrt{21}+6\sqrt{21}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15\sqrt{42}-15\sqrt{2}-36\sqrt{7}+12\sqrt{3}}{120} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5\sqrt{42}-5\sqrt{2}-12\sqrt{7}+4\sqrt{3}}{40}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3 \sqrt{14}- \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 5 \sqrt{3}- 2 \sqrt{18}\right) } \cdot \left( 3 \sqrt{14}- \sqrt{6}\right) = \color{blue}{ 5 \sqrt{3}} \cdot 3 \sqrt{14}+\color{blue}{ 5 \sqrt{3}} \cdot- \sqrt{6}\color{blue}{- 2 \sqrt{18}} \cdot 3 \sqrt{14}\color{blue}{- 2 \sqrt{18}} \cdot- \sqrt{6} = \\ = 15 \sqrt{42}- 15 \sqrt{2}- 36 \sqrt{7} + 12 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \left( 3 \sqrt{14} + \sqrt{6}\right) } \cdot \left( 3 \sqrt{14}- \sqrt{6}\right) = \color{blue}{ 3 \sqrt{14}} \cdot 3 \sqrt{14}+\color{blue}{ 3 \sqrt{14}} \cdot- \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot 3 \sqrt{14}+\color{blue}{ \sqrt{6}} \cdot- \sqrt{6} = \\ = 126- 6 \sqrt{21} + 6 \sqrt{21}-6 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 3. |
This page was created using
Rationalize Denominator Calculator