1 divided by 1+ sqr root 2Rationalise the denominator in each expression

We have to rationalize the denominator in 1 / ( 1 + sqrt
2)

This can be done by multiplying the numerator and
denominator by (1 - sqrt 2). Using the relation (a - b)(a + b) = a^2 - b^2 gives a
rational denominator

1 / ( 1 + sqrt
2)

=> (1 - sqrt 2) / ( 1 + sqrt 2)*(1 - sqrt
2)

=> (1 - sqrt 2) / ( 1^2 - (sqrt
2)^2)

=> (1 - sqrt 2) / ( 1 -
2)

=> (1 - sqrt 2) /
-1

=> - (1 - sqrt
2)

=> sqrt 2 -
1

The required result is: sqrt 2 -
1