Question

Rationalize the denominator 1 / 1 + root 2 + root 3

Answer 1

This is a question of rationalisation of denominator.
Now my solution:
1(1+22√+3√)1(1+22+3)
For rationalising the denominator of 3 terms, multiply the numerator and denominator by the same denominator term but change the sign of 3rd value. It gives
1+22√−3√(1+22√)2−(3√)21+22−3(1+22)2−(3)2
(Consider the first two values of denominator as aa and the third value as bb, then you can apply the property (a+b)(a−b)=a2−b2(a+b)(a−b)=a2−b2, this will give the above expression of denominator)
This gives
1+22√−3√1+8+42√−31+22−31+8+42−3
1+22√−3√6+42√1+22−36+42
Now again the denominator is irrational, therefore again we need to do rationalisation. This time it is a term of 2 values, multiply the numerator and denominator by the same denominator term but change the sign of 2nd term.
1+2
1+22√−3√(6−42√)36−321+22−3(6−42)36−32
6+122√−63√−42√−16+46√46+122−63−42−16+464
−10+82√+46√−63√4−10+82+46−634
Take 2 common from numerator and cancel by denominator. You will get your answer as
−5+42√+26√−33√2−5+42+26−332
The approximated value is 0.1798410.179841(courtesy of my phone calculator).

I HOPE IT WILL HELP YOU DEAR
THANKU
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