Question

Rationalise the denominator

Answer 1

Heya !!!

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

On rationalizing the denominator we get,

$= \frac{ \sqrt{2} - 1 }{ \sqrt{2} + 1 } \times \frac{ \sqrt{2} - 1}{ \sqrt{2} - 1 } \\ \\ = \frac{ {( \sqrt{2} - 1) }^{2} }{ ( \sqrt{2} + 1)( \sqrt{2} - 1) }$

Using the identities :

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

$= \frac{ {( \sqrt{2} )}^{2} + {(1)}^{2} - 2( \sqrt{2} )(1)}{ {( \sqrt{2}) }^{2} - {(1)}^{2} } \\ \\ = \frac{2 + 1 - 2 \sqrt{2} }{2 - 1} \\ \\ = 3 - 2 \sqrt{2}$

Hope this helps ☺

Answer 2

Answer:

Question

To rationalise the denominatir given in the picture = √2 - 1/√2 + 1

Answer

as we know to rationalise the denominator we multiply the same number by both numerator and denominator by changing the sign ..

Solution in picture