Question
Answer
$$\dfrac{1}{4}\sqrt{54}-\dfrac{1}{4}\sqrt{150}=(-\dfrac{1}{2})\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{4}\sqrt{54}-\frac{1}{4}\sqrt{150}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3}{4}\sqrt{6}+(-\frac{5}{4})\sqrt{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(-\frac{1}{2})\sqrt{6}\end{aligned} $$ | |
| ① | $$ \frac{ 1 }{ 4 } \sqrt{ 54 } =
\frac{ 1 }{ 4 } \sqrt{ 3 ^2 \cdot 6 } =
\frac{ 1 }{ 4 } \sqrt{ 3 ^2 } \, \sqrt{ 6 } =
\frac{ 1 }{ 4 } \cdot 3 \sqrt{ 6 } =
\frac{ 3 }{ 4 } \sqrt{ 6 } $$ |
| ② | $$ - \frac{ 1 }{ 4 } \sqrt{ 150 } =
-\frac{ 1 }{ 4 } \sqrt{ 5 ^2 \cdot 6 } =
-\frac{ 1 }{ 4 } \sqrt{ 5 ^2 } \, \sqrt{ 6 } =
-\frac{ 1 }{ 4 } \cdot 5 \sqrt{ 6 } =
-\frac{ 5 }{ 4 } \sqrt{ 6 } $$ |
| ③ | Combine like terms |
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