Solve-
6^2+3^2=AB^2 What is the length of AB in the simplest radical form?

 6^2+3^2-(a*b^2)=0

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    6^2+3^2-(a*b^2)=0  

STEP

1

:

Equation at the end of step

1

:

 ((62) +  32) -  ab2  = 0  

STEP

2

:

2.1     6 = 2•3

(6)2 = (2•3)2 = 22 • 32

Equation at the end of step

2

:

 ((22•32) +  32) -  ab2  = 0  

STEP

3

:

Trying to factor as a Difference of Squares

3.1      Factoring:  45-ab2  

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 :  45  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

3

:

 45 - ab2  = 0  

STEP

4

:

Solving a Single Variable Equation

4.1     Solve   -ab2+45  = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

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step-by-step explanation: