Question

5/√18-√7 rationalise by denominator

Answer 1

Step-by-step explanation:

We know that,

(a - b)(a + b) = a² - b²

$\large \bold{ \frac{5}{ \sqrt{18} - \sqrt{7} } }\\ \\ \large \bold{= \frac{5}{( \sqrt{18} - \sqrt{7} )} \times \frac{( \sqrt{18} + \sqrt{7}) }{( \sqrt{18} + \sqrt{7} )} }\\ \\ \large \bold{ = \frac{5(\sqrt{18} + \sqrt{7})}{ {( \sqrt{18} )}^{2} - {( \sqrt{7} )}^{2} } } \\ \\ \large \bold{= \frac{5( 3\sqrt{2} + \sqrt{7} )}{18 - 7} }\\ \\ \large \bold{ = \red{ \frac{15 \sqrt{2} + 5 \sqrt{7} }{11} }}$