Question

If a=5-2√6 then find the value of √a-1/√a

Answer 1

It bears repeating: you should have applied the well-known following formulas: "Hello", "Please" and "Thanks". 
Anyway... 

= = = = = = = = = = = = = = = = = = 
Yo have 
   A = 5 + 2√6 
      = 3 + 2(√3)×(√2) + 2   ←←← Since √(ab)=(√a)(√b) 
      = (√3)² + 2×(√3)×(√2) × (√2)²   ←←← Since a=(√a)² 
      = (√3 + √2)²    ←←← Since x²+2xy+y²=(x+y)² 

Thus: 
   √A = √3 + √2 

And: 
   1/√A = 1/(√3 + √2) 
      = (√3 – √2) / [(√3 + √2)(√3 – √2)]   ←←← Since (1/x)=y/(xy) 
      = (√3 – √2) / [(√3)² – (√2)²]   ←←← Since (x+y)(x–y)=x²–y² 
      = (√3 – √2) / (3 – 2)    ←←← Since (√a)²=a 
      = (√3 – √2) / 1 
      = √3 – √2 

Thus finally: 
   √A + 1/√A = (√3 + √2) + (√3 – √2) = 2√3 
hope this helps
plz mark it as the brainliest answer

Answer 2

@
a=5-2√6
1/a=(1/5-2√6)
=>1×(5+2√6)/5-2√6×(5+2√6)
=>5+2√6/25-24
=>5+2√6
_____________
a+1/a=(5-2√6)+(5+2√6)=10
(√a)²+(1/√a)²=10
(√a-1/√a)²=√a²+1/√a²-2
(√a-1/√a)²=10-2
(√a-1/√a)²=8
√a-1/√a=±√8
@:-)