Question
Answer
$$\dfrac{3\sqrt{3}\sqrt{165}}{1}=9\sqrt{55}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{3}\sqrt{165}}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3\sqrt{495} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\cdot \sqrt{ 9 \cdot 55 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3\cdot \sqrt{ 9 } \cdot \sqrt{ 55 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3\cdot3 \sqrt{ 55 } \xlongequal{ } \\[1 em] & \xlongequal{ }9\sqrt{55}\end{aligned} $$ | |
| ① | Remove 1 from denominator. |
| ② | Factor out the largest perfect square of 495. ( in this example we factored out $ 9 $ ) |
| ③ | Rewrite $ \sqrt{ 9 \cdot 55 } $ as the product of two radicals. |
| ④ | The square root of $ 9 $ is $ 3 $. |
This page was created using
Rationalize Denominator Calculator