Question

For this test remember all questions have two answers. Please put the smaller answer in the first blank. Solve. x2=12

Answer 1

2.1      Solve  :    x2-12 = 0

Add  12  to both sides of the equation :

                     x2 = 12

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 12  

Can  √ 12 be simplified ?

Yes!   The prime factorization of  12   is

  2•2•3

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 12   =  √ 2•2•3   =

               ±  2 • √ 3

The equation has two real solutions  

These solutions are  x = 2 • ± √3 = ± 3.4641 /This is the answer