Question

Remove the irrationality in the denominator of 1/1+√2+√3​

Answer 1

Given:

• 1/1+√2+√3.

To Do:

• Remove the irrationality of denominator.

Answer:

We have ,

= 1/1+√2+√3.

= 1/ (1)+(√2+√3).

= 1× [(1)+(√2+√3)]/ [(1)+(√2+√3)] × [(1)-(√2+√3)].

= (1)+(√2+√3) / (1)² - (√2+√3)².

= (1)+(√2+√3) / 1 - (2 + 3 + 2√3).

= 1+√2+√3 / 1 - 5 -2√3.

= 1+√2+√3 / -4-2√3

= (1+√2+√3 )(-4+2√3)/(-4-2√3)(-4+2√3)

= (1+√2+√3)(-4+2√3)/(-4)²-(2√3)²

= (1+√2+√3)(-4+2√3)/ 16 - 12.

= (1+√2+√3)(-4+2√3)/4