Question

final exam
100 points possible answered: 0/17
question 1
simplify. assume all variables represent positive values.
$-7\sqrt{12x} + 10\sqrt{27x} = $

Explanation:

Step1: Simplify each square root

Simplify \(\sqrt{12x}\) and \(\sqrt{27x}\). We know that \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) for \(a,b\geq0\). So, \(\sqrt{12x}=\sqrt{4\times3x}=\sqrt{4}\times\sqrt{3x} = 2\sqrt{3x}\) and \(\sqrt{27x}=\sqrt{9\times3x}=\sqrt{9}\times\sqrt{3x}=3\sqrt{3x}\).

Step2: Substitute back into the expression

Substitute the simplified square roots into the original expression: \(-7\sqrt{12x}+10\sqrt{27x}=-7\times2\sqrt{3x}+10\times3\sqrt{3x}\).

Step3: Perform the multiplications

Calculate the multiplications: \(-7\times2\sqrt{3x}=-14\sqrt{3x}\) and \(10\times3\sqrt{3x}=30\sqrt{3x}\).

Step4: Combine like terms

Combine the terms with \(\sqrt{3x}\): \(-14\sqrt{3x}+30\sqrt{3x}=(-14 + 30)\sqrt{3x}=16\sqrt{3x}\).

Answer:

\(16\sqrt{3x}\)