Explanation

This tests the identity for the square root of a surd of the form a + 2√b, but here the coefficient 6 is handled by assuming the root is (p + √q). Squaring gives (3 + √7)² = 9 + 7 + 6√7 = 16 + 6√7, which matches exactly, so the positive square root is 3 + √7. Hence option (c). The distractors fail the expansion check: (4 + √7)² = 23 + 8√7 and (3 − √7)² also equals 16 − 6√7, not 16 + 6√7, so the sign matters.