Question

What is the square root

Answer 1

Answer:

Step-by-step explanation:

Trying to factor as a Difference of Squares :

1.1      Factoring:  r2-96

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 96 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  1  :

 r2 - 96  = 0

Step  2  :

Solving a Single Variable Equation :

2.1      Solve  :    r2-96 = 0

Add  96  to both sides of the equation :

                     r2 = 96

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

                     r  =  ± √ 96  

Can  √ 96 be simplified ?

Yes!   The prime factorization of  96   is

  2•2•2•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).

√ 96   =  √ 2•2•2•2•2•3   =2•2•√ 6   =

               ±  4 • √ 6

The equation has two real solutions  

These solutions are  r = 4 • ± √6 = ± 9.7980  

Two solutions were found :

                  r = 4 • ± √6 = ± 9.7980

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