Question
Answer
$$\dfrac{\sqrt{972}}{4}=\dfrac{9\sqrt{3}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{972}}{4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{ \sqrt{ 324 \cdot 3 } }{ 4 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ \sqrt{ 324 } \cdot \sqrt{ 3 } }{ 4 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{18\sqrt{3}}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 18 \cdot \sqrt{ 3 } : \color{orangered}{ 2 }}{ 4 : \color{orangered}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{9\sqrt{3}}{2}\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 972. ( in this example we factored out $ 324 $ ) |
| ② | Rewrite $ \sqrt{ 324 \cdot 3 } $ as the product of two radicals. |
| ③ | The square root of $ 324 $ is $ 18 $. |
| ④ | Divide numerator and denominator by $ \color{orangered}{ 2 } $. |
This page was created using
Simplify Radical Expression