To simplify the expression [tex]\(14 \sqrt{6} - 6 \sqrt{24}\)[/tex], follow these steps:
1. Simplify each term separately.
- The first term [tex]\(14 \sqrt{6}\)[/tex] is already in its simplest form.
- For the second term [tex]\(6 \sqrt{24}\)[/tex], we need to simplify [tex]\(\sqrt{24}\)[/tex]:
[tex]\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2 \sqrt{6}
\][/tex]
2. Rewrite the second term using the simplified form of [tex]\(\sqrt{24}\)[/tex]:
[tex]\[
6 \sqrt{24} = 6 \times 2 \sqrt{6} = 12 \sqrt{6}
\][/tex]
3. Substitute the simplified forms back into the original expression:
[tex]\[
14 \sqrt{6} - 12 \sqrt{6}
\][/tex]
4. Combine like terms:
Since both terms have [tex]\(\sqrt{6}\)[/tex] as a common factor, we factor out [tex]\(\sqrt{6}\)[/tex]:
[tex]\[
14 \sqrt{6} - 12 \sqrt{6} = (14 - 12) \sqrt{6} = 2 \sqrt{6}
\][/tex]
Therefore, the simplified expression is [tex]\(2 \sqrt{6}\)[/tex].
In this form:
- The coefficient [tex]\(a = 2\)[/tex],
- The radicand [tex]\(b = 6\)[/tex].
