Question

Q no 4. Rationalise the denominator and
simplify:
a) (root3-root2)/(root3+root2)​

Answer 1

QUESTION:

RATIONALISE THE DENOMINATOR :

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

ANSWER:

In order to rationalise we use the rationalising factor .

then we multiply with the rationalising factor in both numerator and denominator.

Here the rationalising factor is

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

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

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

OPENING THE IDENTITY HERE

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

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

$5 - 2 \sqrt{6}$

WE USE IDENTITY HERE :

$( {x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy$

${x}^{2} - {y}^{2} = (x - y)(x + y)$

FINAL ANSWER :

$5 - 2 \sqrt{6}$

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