Question

If x=7+√40, find the value of√x + 1/√x

Answer 1

(√x+1/√x)^2=x+1/x+2
=7+√40+(1/7+√40)+2
=7+√40+((7-√40)/9)+2
=(81+9√40+7-√40)/9
=(88+8√40)/9
(√x+1/√x)=√(88+8√40)/3

Answer 2

x=7+√40

=7+2√10

=5+2+2√10

=(√5)²+2.√5.√2+(√2)²

=(√5+√2)²

∴√x=√5+√2 (neglecting the negative sign)

1/√x=1/(√5+√2)

=(√5-√2)/(√5+√2)(√5-√2)

=(√5-√2)/(5-2)

=(√5-√2)/3

√x+1/√x

=(√5+√2)+(√5-√2)/3

=(3√5+3√2+√5-√2)/3

=(4√5+2√2)/3

=2(2√5+√2)/3