Simplifying Nested Radicals

This video solves a question on simplifying nested radicals. This is a quite challenging problem.

[ilyashick]

Nice solution, sir In my view (6^1/2-(20^1/2)^1/2 is equal 6^1/2 - (2^1/2 of 5)^1/2. from this point ((6 - 2^1/2 of 5)^1/2 rest of them follow your steps.

[tassiedevil]

alternatively by directly squaring the initial expression: 6 - root 20 = m -2 n root m +n^2, so 6=m+n^2 and root 20 (=2 root 5) = 2 n root m, so n=1 and m=5.