Question
Answer
$$\dfrac{\sqrt{7}-1}{5\sqrt{35}}=\dfrac{7\sqrt{5}-\sqrt{35}}{175}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{7}-1}{5\sqrt{35}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{7}-1}{5\sqrt{35}}\frac{\sqrt{35}}{\sqrt{35}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7\sqrt{5}-\sqrt{35}}{175}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{35}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{7}-1\right) } \cdot \sqrt{35} = \color{blue}{ \sqrt{7}} \cdot \sqrt{35}\color{blue}{-1} \cdot \sqrt{35} = \\ = 7 \sqrt{5}- \sqrt{35} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{35} } \cdot \sqrt{35} = 175 $$ |
This page was created using
Rationalize Denominator Calculator