Question

if x=9 + 4√5,then find √x-√1/x

Answer 1

x=9+4√5
1/x=9-4√5 {after conjugate steps}
(√x-1/√x)² =(√x)² - 2(√x)(1/√x) +(1/√x)²
= x +1/x -2
=(9+4√5)+(9-4√5)-2
= 18-2
(√x-1/√x)² =16
√x-1/√x =√16=4

Hope it helps