Express each one of the following with rational denominator: (i) 30/5√3 - 3√5 (ii) 1/2√5 - √3

Question

Express each one of the following with rational denominator:

(i) \(\frac{30}{5\sqrt3-3\sqrt5}\)

(ii) \(\frac{1}{2\sqrt5-\sqrt3}\)

(iii) \(\frac{\sqrt3+1}{2\sqrt2-\sqrt3}\)

Answer 1

(i) we have \(\frac{30}{5\sqrt3-3\sqrt5}\) to rationalize factor of 5√3 - 3√5 is 5√3 + 3√5

 

(ii) we have \(\frac{1}{2\sqrt5-\sqrt3}\) to rationalize factor of 2√5 - √3 is 2√5 + √3

(iii) we have \(\frac{\sqrt3+1}{2\sqrt2-\sqrt3}\) to rationalize factor of 2√2 - √3 is 2√2 + √3