Question

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1. which expression is equivalent to \\(\sqrt{75x^3} - \sqrt{27x^3}\\), if \\(x > 0\\)?

a \\(4x\sqrt{6x}\\)
b \\(4x\sqrt{3x}\\)
c \\(2x\sqrt{6x}\\)
d \\(2x\sqrt{3x}\\)

Explanation:

Step1: Simplify √(75x³)

Factor into perfect squares: √(25×3×x²×x) = 5x√(3x)

Step2: Simplify √(27x³)

Factor into perfect squares: √(9×3×x²×x) = 3x√(3x)

Step3: Subtract the two expressions

5x√(3x) - 3x√(3x) = 2x√(3x)

Answer:

D 2x√3x