Question
Answer
$$9\cdot\dfrac{\sqrt{2}}{\sqrt{18}}=3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9 \cdot \frac{\sqrt{2}}{\sqrt{18}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9\cdot\frac{6}{18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9 \cdot \frac{ 6 : \color{orangered}{ 6 } }{ 18 : \color{orangered}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }9\cdot\frac{1}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{18} = 6 $$ Simplify denominator. $$ \color{blue}{ \sqrt{18} } \cdot \sqrt{18} = 18 $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 6 } $. |
| ③ | Multiply $9$ by $ \dfrac{1}{3} $ to get $ 3$. Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Cancel down by $ \color{blue}{3} $ $$ \begin{aligned} 9 \cdot \frac{1}{3} & = \frac{9}{\color{red}{1}} \cdot \frac{1}{3} = \frac{9 : \color{blue}{3}}{3 : \color{blue}{3}} = \\[1ex] &= \frac{3}{1} =3 \end{aligned} $$ |
This page was created using
Simplify Radical Expression