To solve the given expression [tex]\( 18 \sqrt{3} - 5 \sqrt{12} \)[/tex], we'll follow these steps:
1. Simplify Each Term:
- The first term is straightforward, [tex]\( 18 \sqrt{3} \)[/tex].
- For the second term, we'll simplify [tex]\( \sqrt{12} \)[/tex].
Notice that [tex]\( \sqrt{12} \)[/tex] can be simplified as follows:
[tex]\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2 \sqrt{3}
\][/tex]
- Substitute [tex]\( \sqrt{12} \)[/tex] in the expression,
[tex]\[
-5 \sqrt{12} = -5 (2 \sqrt{3}) = -10 \sqrt{3}
\][/tex]
2. Combine the Like Terms:
- Now we add the terms [tex]\( 18 \sqrt{3} \)[/tex] and [tex]\( -10 \sqrt{3} \)[/tex]:
[tex]\[
18 \sqrt{3} - 10 \sqrt{3} = (18 - 10) \sqrt{3} = 8 \sqrt{3}
\][/tex]
Based on the equivalent numerical values:
- [tex]\( 18 \sqrt{3} \approx 31.17691453623979 \)[/tex]
- [tex]\( -5 \sqrt{12} \approx -17.32050807568877 \)[/tex]
- After combining:
[tex]\[
31.17691453623979 - 17.32050807568877 = 13.856406460551018
\][/tex]
So, the simplified and combined term is:
[tex]\[
8 \sqrt{3} \approx 13.856406460551018
\][/tex]
Thus, the combined expression [tex]\( 18 \sqrt{3} - 5 \sqrt{12} \)[/tex] simplifies to [tex]\( 8 \sqrt{3} \approx 13.856406460551018 \)[/tex].
