Question

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

Answer 1

a = 7 -4√3

1/a = 1/( 7 -4√3) = (7-4√3)/(7-4√3)(7+4√3)
=(7+4√3)/(49-48) = (7+4√3)

so, √a = √( 7 -4√3)
= √(2²+√3²-2.2√3)
=√(2 -√3)² = ( 2 -√3)

same way ,
1/√a = √(2² +√3² +2.2√3)
=√(2+√3)²
=(2 +√3)

now ,

√a + 1/√a = (2 -√3) + (2 + √3) = 4

Answer 2

a=7-4 root 3 find the value of root a + 1/root a

..Thus value of

$\sqrt{a} + \frac{1}{ \sqrt{a} } = 4$