Question
Answer
$$\dfrac{\sqrt{1}+\sqrt{1}\cdot\dfrac{5}{\sqrt{1}}\cdot7}{\sqrt{2}}=18\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{1}+\sqrt{1}\cdot\frac{5}{\sqrt{1}}\cdot7}{\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{1+35}{1}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{36}{1}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\frac{36}{1}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{36\sqrt{2}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ }18\sqrt{2}\end{aligned} $$ | |
| ① | $$ \sqrt{1}+\sqrt{1}\cdot\frac{5}{\sqrt{1}}\cdot7
= 1 \cdot \color{blue}{\frac{ 1 }{ 1}} + 35 \cdot \color{blue}{\frac{ 1 }{ 1}}
= \frac{1+35}{1} $$ |
| ② | Simplify numerator $$ \color{blue}{1} + \color{blue}{35} = \color{blue}{36} $$ |
| ③ | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}} $$. |
| ④ | Multiply in a numerator. $$ \color{blue}{ 36 } \cdot \sqrt{2} = 36 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{2} = 2 $$ |
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