1+2 sqrt3 / 1+sqrt3?

Answer 1

[ (1 + 2√3)(1 - √3) ] / [ (1 + √3)(1 - √3) ]
( 1 + √3 - 6 ) / (1 - 3)
(√3 - 5) / ( - 2 )
(1 / 2) (5 - √3)

Answer 2

(1+2 sqrt3 / 1+sqrt3)(1-sqrt3/1-sqrt3)
= -5 + sqrt3/ -2

Answer 3

(1+2 sqrt3)/ (1+sqrt3)
= (1+2sqrt3)(1-sqrt3)/(1-3)
= (1+sqrt3-6)/(-2)
=2.5 - .5sqrt3

Answer 4

1+2 sqrt3 / 1+sqrt3
multiply the nr & dr 1-sqrt3
[(1+2 sqrt3)(1-sqrt3)] /[(1+sqrt3)(1-sqrt3)]
[(1+2 sqrt3-sqrt3-2{sqrt3}^2)] /[(1-{sqrt3}^2)]
[(1+sqrt3-2)] /[(1-3)]
[(sqrt3-1)] /[(-2)]
[-1+sqrt3] /[-2]

Answer 5

1 + 2 sqrt(3) / 1 + sqrt(3)

we have a + sqrt(b) at the denum
if we multiply it with a - sqrt(b) we will get rid
of the sqrts at the denum.
[a+sqrt(b)] * [a -sqrt(b)] = a^2 - b.

So lets do that trick here,
= [1+2sqrt(3)]*[1-sqrt(3)] / [1+sqrt(3)]*[1-sqrt(3)]
Now one more thing,
(a - b)*(c-d) = ac - ad - bc + bd

Rewriting the previous equation we have :
=[1- sqrt(3) + 2sqrt(3) - 2sqrt(3)sqrt(3)] / (1 -3)
=[1+sqrt(3)-2*3]/-2
=[-5+sqrt(3)] / -2
= [5-sqrt(3)] / 2

now comes the calculator if you want
=1.6339746

Answer 6

1.63 (2.d.p)