Question

what is the value of fourth root of
(6+ 2 root 5) (6-2 root 5) ?

a) 1
b) 2
c) 4
d) 8

Answer 1

Answer:

c) 4

Let

√(5+2√6=√x+√y  

5+2√6=x+y+2√xy  

x+y=5 , xy=6  

From here get the value of x-y which will be 1.

You can do that by gettimg  x2+y2=13  

(x−y)2=1  From there it follows that

x−y=1  

now solve a simultaneous to get x= 3, y = 2

therefore Answer is

√3+√2