MATH SOLVE

3 months ago

Q:
# What is the square root

Accepted Solution

A:

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 - B2Note : 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 • √ 6The equation has two real solutions These solutions are r = 4 • ± √6 = ± 9.7980 Two solutions were found : r = 4 • ± √6 = ± 9.7980Processing ends successfully