Simplify the following expression:$(3 + \sqrt{3})(2 + \sqrt{2})$

Given:

The given expression is $(3+\sqrt{3})(2+\sqrt{2})$.

To do :

We have to simplify the given expression.

Solution :

We know that,

$(a+b) \times (c+d) = a(c+d) +b(c+d) = ac+ad+bc+bd$

Therefore,

$(3+\sqrt{3})(2+\sqrt{2})= (3)(2) + 3(\sqrt{2})+(\sqrt{3})(2)+(\sqrt{3})(\sqrt{2})$

                                           $= 6+3\sqrt{2}+2\sqrt{3}+\sqrt{6}$

The simplified form of $(3+\sqrt{3})(2+\sqrt{2})$ is $6+3\sqrt{2}+2\sqrt{3}+\sqrt{6}$

Tutorialspoint

Updated on: 10-Oct-2022

42 Views

Kickstart Your Career

Get certified by completing the course

Get Started