What is √(17 - 4√15) + √(8 - 2√15) equal to?

17 - 4√15 = 12 + 5 - 2·2√15 = (2√3)² + (√5)² - 2(2√3)(√5) = (2√3 - √5)². So √(17 - 4√15) = 2√3 - √5 (assuming 2√3 > √5; 2√3 ≈ 3.46, √5 ≈ 2.24, yes). Wait, we want the positive form. Actually let me try: 17 - 4√15 = 15 + 2 - 2·2√15... Try (√15 - √2)² = 15 + 2 - 2√30, no. Try (√a - √b)² = a + b - 2√(ab) = 17 - 4√15 = 17 - 2√60, so a+b=17, ab=60: a=12,b=5. So √(17-4√15) = √12 - √5 = 2√3 - √5. Similarly 8 - 2√15: a+b=8, ab=15: a=5,b=3. So √(8-2√15) = √5 - √3. Sum = 2√3 - √5 + √5 - √3 = √3. Hmm, that gives √3, answer (a). Let me recheck: 2√3 - √5 + √5 - √3 = √3. So answer is (a) √3.