What is the square root of 15-4\sqrt{14}?
- A. 2\sqrt{2}-\sqrt{7} ✓
- B. 3\sqrt{2}-2\sqrt{7}
- C. \sqrt{15}-\sqrt{7}
- D. \sqrt{5}-\sqrt{3}
Correct Answer: A. 2\sqrt{2}-\sqrt{7}
Explanation
We need \sqrt{15-4\sqrt{14}} = \sqrt{15-2\sqrt{56}}. Find two numbers whose sum is 15 and product is 56, which are 8 and 7. Thus, it simplifies to \sqrt{(\sqrt{8}-\sqrt{7})^2} = \sqrt{8}-\sqrt{7} = 2\sqrt{2}-\sqrt{7}.
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