Rationalies the denominator and simplify : (i) √3 - √2/√3 + √2 (ii) 5 + 2√3/7 + 4√3 (iii) 1 + √2/3 - 2√2

Question

Rationalies the denominator and simplify:

(i) \(\frac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2}\)

(ii) \(\frac{5+2\sqrt3}{7+4\sqrt3}\)

(iii) \(\frac{1+\sqrt2}{3-2\sqrt2}\)

Answer 1

(i) \(\frac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2}\) = \(\frac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2}\) x \(\frac{\sqrt3-\sqrt2}{\sqrt3-\sqrt2}\) = \(\frac{3+2-2\sqrt6}{3-2}\) = 5 - 2√6

(ii) \(\frac{5+2\sqrt3}{7+4\sqrt3}\) = \(\frac{5+2\sqrt3}{7+4\sqrt3}\) x \(\frac{7-4\sqrt3}{7-4\sqrt3}\) = \(\frac{35+14\sqrt3-20\sqrt3-24}{49-48}\) = 11-6√3

(iii) \(\frac{1+\sqrt2}{3-2\sqrt2}\) = \(\frac{1+\sqrt2}{3-2\sqrt2}\) x \(\frac{3+2\sqrt2}{3+2\sqrt2}\) = \(\frac{3+3\sqrt2+2\sqrt2+4}{9-8}\) = 7 + 5√2