Question

simplify the expression: \frac{\sqrt{300x}}{\sqrt{x}}

a) \frac{\sqrt{3}}{10}
b) 10x\sqrt{3}
c) 10\sqrt{3}
d) \frac{10\sqrt{3}}{x}

question 14 (5 points)
simplify: \sqrt{18} - \sqrt{24} + \sqrt{54}

a) 3\sqrt{2} + \sqrt{6}
b) -\sqrt{6} + 2\sqrt{9}
c) 4\sqrt{3}
d) 10\sqrt{10}

question 15 (5 points)
simplify the expression: \frac{4}{\sqrt{2}}

a) 2\sqrt{2}
b) \sqrt{2}
c) 4\sqrt{2}
d) \frac{\sqrt{2}}{2}

Explanation:

Simplify the first expression

$$ \frac{\sqrt{300x}}{\sqrt{x}} = \sqrt{\frac{300x}{x}} = \sqrt{300} = \sqrt{100 \times 3} = 10\sqrt{3} $$

Simplify the second expression

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Simplify the third expression

$$ \frac{4}{\sqrt{2}} = \frac{4\sqrt{2}}{\sqrt{2}\sqrt{2}} = \frac{4\sqrt{2}}{2} = 2\sqrt{2} $$

Answer:

Question 1

• (A) \(\frac{\sqrt{3}}{10}\)
• (B) \(10x\sqrt{3}\)
• (C) \(10\sqrt{3}\) (Correct answer)
• (D) \(\frac{10\sqrt{3}}{x}\)

Question 2

• (A) \(3\sqrt{2} + \sqrt{6}\) (Correct answer)
• (B) \(-\sqrt{6} + 2\sqrt{9}\)
• (C) \(4\sqrt{3}\)
• (D) \(10\sqrt{10}\)

Question 3

• (A) \(2\sqrt{2}\) (Correct answer)
• (B) \(\sqrt{2}\)
• (C) \(4\sqrt{2}\)
• (D) \(\frac{\sqrt{2}}{2}\)