Question
Answer
$$5\sqrt{60}-\sqrt{135}+3\sqrt{75}=7\sqrt{15}+15\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{60}-\sqrt{135}+3\sqrt{75}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10\sqrt{15}-3\sqrt{15}+15\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}7\sqrt{15}+15\sqrt{3}\end{aligned} $$ | |
| ① | $$ 5 \sqrt{60} =
5 \sqrt{ 2 ^2 \cdot 15 } =
5 \sqrt{ 2 ^2 } \, \sqrt{ 15 } =
5 \cdot 2 \sqrt{ 15 } =
10 \sqrt{ 15 } $$ |
| ② | $$ - \sqrt{135} =
- \sqrt{ 3 ^2 \cdot 15 } =
- \sqrt{ 3 ^2 } \, \sqrt{ 15 } =
- 3 \sqrt{ 15 }$$ |
| ③ | $$ 3 \sqrt{75} =
3 \sqrt{ 5 ^2 \cdot 3 } =
3 \sqrt{ 5 ^2 } \, \sqrt{ 3 } =
3 \cdot 5 \sqrt{ 3 } =
15 \sqrt{ 3 } $$ |
| ④ | Combine like terms |
This page was created using
Simplify Radical Expression