Rationalise the denominators of the following: (i) 1/√7 (ii) 1/(√7 - √6) (iii) 1/(√5 + √2) (iv) 1/(√7 + 2)

(1) 1/√7 = 1/√7 × √7/√7 (multiplying and dividing by √7) = √7/7
(2) 1/(√7 - √6) = 1/(√7 - √6) × (√7 + √6)/(√7 + √6) (multiplying and dividing by √7 + √6) = (√7 + √6)/7 - 6 = √7 + √6
(3) 1/(√5 + √2) = 1/(√5 + √2) × (√5 - √2)/(√5 - √2) (multiplying and dividing by √5 - √2) = (√5 - √2)/5 - 2 = (√5 - √2)/3
(4) 1/(√7 + 2) = 1/(√7 + 2) × (√7 - 2)/(√7 - 2) (multiplying and dividing by √7 - 2) = (√7 - 2)/7 - 4 = (√7 - 2)/3