Question
Answer
$$5\sqrt{108}-5\sqrt{27}=15\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{108}-5\sqrt{27}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}30\sqrt{3}-15\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}15\sqrt{3}\end{aligned} $$ | |
| ① | $$ 5 \sqrt{108} =
5 \sqrt{ 6 ^2 \cdot 3 } =
5 \sqrt{ 6 ^2 } \, \sqrt{ 3 } =
5 \cdot 6 \sqrt{ 3 } =
30 \sqrt{ 3 } $$ |
| ② | $$ - 5 \sqrt{27} =
-5 \sqrt{ 3 ^2 \cdot 3 } =
-5 \sqrt{ 3 ^2 } \, \sqrt{ 3 } =
-5 \cdot 3 \sqrt{ 3 } =
-15 \sqrt{ 3 } $$ |
| ③ | Combine like terms |
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