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

justaguide | Certified Educator

calendarEducator since 2010

starTop subjects are Math, Science, and Business

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

check Approved by eNotes Editorial

## Related Questions

academicsfirst | Certified Educator

calendarEducator since 2011

starTop subjects are Math and Literature

The question asks us to rationalize the denominator in the expression 1 divided by 1 + sqrt 2.

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

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

=> (1 - sqrt 2)/-1

=> -1 + sqrt 2

The answer is -1 + sqrt 2.

check Approved by eNotes Editorial