Question

If √2 = 1.414 and √3 = 1.734 then find the value of 1

√3+√2

by rationalizing the denominator.​

Answer 1

Answer:

$\frac{1}{ \sqrt{3} + \sqrt{2} } = \frac{1}{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ = \frac{ \sqrt{3} - \sqrt{2} }{ { \sqrt{3} }^{2} - { \sqrt{2} }^{2} } \\ = \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} \\ = \sqrt{3} - \sqrt{2} \\ = 1.73 - 1.41 \\ = 0.32$