Question

Rationalise the denominator of 2+√3 / 2-√3

Answer 1

Solution is attached below :-..

Answer 2

Given,

• 2+√3 / 2-√3 is given.

To find,

• We have to rationalize the denominator.

Solution,

We can rationalize the denominator of 2+√3 / 2-√3 by multiplying and dividing it by its rationalizing factor.

Rationalization is the process by which roots are removed from the denominator by transferring them to the numerator.

                  2+√3 / 2-√3

Multiplying and dividing the given fraction by its rationalizing factor (2+$\sqrt{3}$), we get

                   2+$\sqrt{3}$ /2-$\sqrt{3}$ * 2+$\sqrt{3}$/2+$\sqrt{3}$

      Using (a+b)² = a² + b² +2ab and (a+b)(a-b) = a²-b², we get

                   (2+$\sqrt{3}$)²/(2)²-(√3)²

                      (2)² +(√3)² +4√3 / 4-3

                       4 +3 +4√3 / 1

                         7 + 4√3

Hence, 2+√3 / 2-√3 after rationalizing the denominator becomes  7 + 4√3.