Question

1. $3sqrt{24x} - 2sqrt{54x} + sqrt{48}$

Explanation:

Step1: Simplify each radical

Simplify \(3\sqrt{24x}\): \(24x = 4\times6x\), so \(3\sqrt{24x}=3\sqrt{4\times6x}=3\times2\sqrt{6x}=6\sqrt{6x}\)
Simplify \(2\sqrt{54x}\): \(54x = 9\times6x\), so \(2\sqrt{54x}=2\sqrt{9\times6x}=2\times3\sqrt{6x}=6\sqrt{6x}\)
Simplify \(\sqrt{48}\): \(48 = 16\times3\), so \(\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}\)

Step2: Combine like terms

Substitute back: \(6\sqrt{6x}-6\sqrt{6x}+4\sqrt{3}\)
The \(6\sqrt{6x}\) and \(-6\sqrt{6x}\) cancel out.

Answer:

\(4\sqrt{3}\)