Question

if a = 7-4√3, find the value of √a+1/√a

Answer 1

a=7-4√3=2^2 - 2*2*√3 + (√3)^2=(2-√3)^2
so, √a = 2-√3 and 1/√a = 2+√3
so, √a + 1/√a =2 - √3 +2 + √3 = 4

Answer 2

√a=√(7-4√3)
={√(4)^2+√3^2 - 2.√4.√3}
= (√4 -√3)^2
=√4-√3

now √a + √1/a
(√4-√3 )+ 1/(√4-√3)
by rationalizing...((1/√4-√3))==(√4-√3)
therefore
(√4-√3)(√4+√3)
1 ans...
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