Question

(7+root9) l (4+root3)

Answer 1

First of all, notice that

7 + 4 sqrt(3)

= 4 + 2 sqrt(3) + 2 sqrt(3) + 3

= (2 + sqrt(3))^2

Now, since

√x + 1/√x = (x + 1) / sqrt(x),

Substitute 7 + 4 sqrt(3) for x:

= (7 + 4 sqrt(3) + 1) / sqrt(7 + 4 sqrt(3))

Collect terms:

= ( 8 + 4 sqrt(3)) / (2 + sqrt(3))

Factor the numerator:

= 4 [ ( 2 + sqrt(3) ) / (2 + sqrt(3)) ]

= 4 (1)

= 4