Question

The value of \[ \sqrt{1 + \frac{\sqrt{3}}{2}} - \sqrt{1 - \frac{\sqrt{3}}{2}} \text{ is:} \]

• A. \( \sqrt{3} \)
• B. \( 2\sqrt{3} \)
• C. 1
• D. 2

Hint:

When solving square roots, simplify step by step and use approximations for irrational numbers where necessary.

Answer 1

The Correct Option is D

Simplify the expression step by step:
First, evaluate \( \frac{\sqrt{3}}{2} \) and substitute into the square roots: \[ 1 + \frac{\sqrt{3}}{2} \approx 1.866 \quad \text{and} \quad 1 - \frac{\sqrt{3}}{2} \approx 0.134 \] Now take the square roots: \[ \sqrt{1.866} \approx 1.366 \quad \text{and} \quad \sqrt{0.134} \approx 0.366 \] Finally, subtract: \[ 1.366 - 0.366 = 2 \] Thus, the correct answer is 2.