Explanation

Write the root as √a − √b with a, b positive. Squaring gives a + b − 2√(ab) = 23 − 4√15 = 23 − √240, so a + b = 23 and ab = 60. Solving, {a, b} = {20, 3}, so the two square roots are ±(2√5 − √3) = ±(√20 − √3). The positive root 2√5 − √3 is not listed; the listed value √3 − 2√5 = −(2√5 − √3) is the negative square root, and indeed (√3 − 2√5)² = 23 − 4√15. Hence option (c) is the intended answer.