Question
Answer
$$\dfrac{28}{\sqrt{450}+\sqrt{50}}=\dfrac{7\sqrt{2}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{28}{\sqrt{450}+\sqrt{50}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{28}{\sqrt{450}+\sqrt{50}}\frac{\sqrt{450}-\sqrt{50}}{\sqrt{450}-\sqrt{50}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{420\sqrt{2}-140\sqrt{2}}{450-150+150-50} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{280\sqrt{2}}{400} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{ 280 \sqrt{ 2 } : \color{blue}{ 40 } } { 400 : \color{blue}{ 40 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{7\sqrt{2}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{450}- \sqrt{50}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 28 } \cdot \left( \sqrt{450}- \sqrt{50}\right) = \color{blue}{28} \cdot \sqrt{450}+\color{blue}{28} \cdot- \sqrt{50} = \\ = 420 \sqrt{2}- 140 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{450} + \sqrt{50}\right) } \cdot \left( \sqrt{450}- \sqrt{50}\right) = \color{blue}{ \sqrt{450}} \cdot \sqrt{450}+\color{blue}{ \sqrt{450}} \cdot- \sqrt{50}+\color{blue}{ \sqrt{50}} \cdot \sqrt{450}+\color{blue}{ \sqrt{50}} \cdot- \sqrt{50} = \\ = 450-150 + 150-50 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide numerator and denominator by $ \color{blue}{ 40 } $. |
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