Answer :

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].