Question

Rationalise the denominators of: (i) √3-√2/√3+√2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Question :

$\sf \small{rationalise \:the \: denominator } \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

Rationalising :

• To rationalize the denominator, you must multiply both the numerator and the denominator by the conjugate of the denominator.

• Remember to find the conjugate all you have to do is change the sign between the two terms.

• Distribute both the numerator and the denominator.

Solution :

$\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

$\frac{( \sqrt{3} - \sqrt{2} )( \sqrt{3} - \sqrt{2}) }{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2} ) }$

$\frac{ {( \sqrt{3} - \sqrt{2}) }^{2} }{ {( \sqrt{3}) }^{2} - {( \sqrt{2}) }^{2} }$

Using Identity : For numerator and For denominator

(a - b)² = a² - 2ab + b²

(a - b)(a + b) = a² - b²

Here ,

a → √3

b → √2

$\frac{( \sqrt{3})^{2} - 2 \times \sqrt{3} \times \sqrt{2} + {( \sqrt{2}) }^{2} }{3 - 2}$

$\frac{3 - 2 \sqrt{6} + 2 }{1}$

$5 - 2 \sqrt{6}$

• So after rationalising we got the answer as 5 - 2√6