JAMB 2015 · UTME · Q2

Find a square root of $170 - 20\sqrt{30}$ .

Worked solution (try it first)

A square root has the form $a\sqrt5 - b\sqrt6$ , because $(a\sqrt5 - b\sqrt6)^2 = 5a^2 + 6b^2 - 2ab\sqrt{30}$ .
Match the surd parts: $2ab = 20$ , so $ab = 10$ .
Try $a = 2$ , $b = 5$ : $5(4) + 6(25) = 20 + 150$ , which is 170.
That matches, so $(2\sqrt5 - 5\sqrt6)^2 = 170 - 20\sqrt{30}$ , and $2\sqrt5 - 5\sqrt6$ is a square root, option C.