Question
Answer
$$\dfrac{\dfrac{3}{\sqrt{2}}\cdot\dfrac{5}{\sqrt{10}}}{2}=\dfrac{\dfrac{15\sqrt{5}}{10}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{3}{\sqrt{2}}\cdot\frac{5}{\sqrt{10}}}{2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{15}{2\sqrt{5}}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{15}{2\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\frac{15\sqrt{5}}{10}}{2}\end{aligned} $$ | |
| ① | $$ \color{blue}{ 3 } \cdot 5 = 15 $$$$ \color{blue}{ \sqrt{2} } \cdot \sqrt{10} = 2 \sqrt{5} $$ |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ 15 } \cdot \sqrt{5} = 15 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{5} } \cdot \sqrt{5} = 10 $$ |
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