Question

1. $3sqrt{24x} - 2sqrt{54x} + sqrt{48}$
2. $5sqrt{18c} + 3sqrt{72c} + 6sqrt{76}$

Explanation:

Step1: Simplify \(3\sqrt{24x}\)

Factor 24x: \(24x = 8\times3x = 2^3\times3x\). So, \(3\sqrt{24x}=3\sqrt{8\times3x}=3\times2\sqrt{6x}=6\sqrt{6x}\).

Step2: Simplify \(2\sqrt{54x}\)

Factor 54x: \(54x = 27\times2x = 3^3\times2x\). So, \(2\sqrt{54x}=2\sqrt{27\times2x}=2\times3\sqrt{6x}=6\sqrt{6x}\).

Step3: Simplify \(\sqrt{48}\)

Factor 48: \(48 = 16\times3 = 4^2\times3\). So, \(\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}\).

Step4: Combine like terms

Now, substitute back into the original expression: \(3\sqrt{24x}-2\sqrt{54x}+\sqrt{48}=6\sqrt{6x}-6\sqrt{6x}+4\sqrt{3}\). The \(6\sqrt{6x}\) and \(-6\sqrt{6x}\) cancel out, leaving \(4\sqrt{3}\).

Answer:

\(4\sqrt{3}\)