Question

64 simplify $3sqrt{4x} cdot 7sqrt{3x^2}$

Explanation:

Step1: Multiply coefficients and radicals

Multiply the coefficients \(3\) and \(7\), and multiply the radicals \(\sqrt{4x}\) and \(\sqrt{3x^2}\) using the property \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\). So we have \(3\times7\times\sqrt{4x\cdot3x^2}=21\sqrt{12x^3}\).

Step2: Simplify the radical

Simplify \(\sqrt{12x^3}\). Factor \(12x^3\) as \(4x^2\cdot3x\). Then \(\sqrt{4x^2\cdot3x}=\sqrt{4x^2}\cdot\sqrt{3x}=2x\sqrt{3x}\) (assuming \(x\geq0\) for the square root to be real in the context of simplification).

Step3: Multiply with the coefficient

Multiply \(21\) with \(2x\sqrt{3x}\). So \(21\times2x\sqrt{3x}=42x\sqrt{3x}\).

Answer:

\(42x\sqrt{3x}\)