(i) \(\frac{\sqrt3-1}{\sqrt3+1}\) = a - b √3
Given,
\(\frac{\sqrt3-1}{\sqrt3+1}\) = a - b √3
Rationalising factor for denominator is √3 - 1
On equating rational and irrational parts,
We get a = 2 and b = 1
(ii) \(\frac{4+\sqrt2}{2+\sqrt2}\) = a - √b rationalising factor for the denominator is We have 2 - √2
On equating rational and irrational parts we get,
a = 3 and b = 2
(iii) \(\frac{3+\sqrt2}{3-\sqrt2}\) = a + b √2
Rationalising factor for the denominator is 3 + √2
On equating rational and irrational parts we get,
a = \(\frac{11}{7}\) and b = \(\frac{6}{7}\)
