Taking the Square Root of Both Sides

Taking the Square Root of Both SidesAdapted from Walch Education

Complex NumbersThe imaginary unit i represents the non-real value . i is the number whose square is 1. We define i so that and i 2 = 1. A complex number is a number with a real component and an imaginary component. Complex numbers can be written in the form a + bi, where a and b are real numbers, and i is the imaginary unit. 5.2.1: Taking the Square Root of Both Sides2

Real NumbersReal numbers are the set of all rational and irrational numbers. Real numbers do not contain an imaginary component. Real numbers are rational numbers when they can be written as , where both m and n are integers and n 0. Rational numbers can also be written as a decimal that ends or repeats. 5.2.1: Taking the Square Root of Both Sides3

Irrational NumbersReal numbers are irrational when they cannot be written as , where m and n are integers and n 0. Irrational numbers cannot be written as a decimal that ends or repeats. The real number is an irrational number because it cannot be written as the ratio of two integers. examples of irrational numbers include and .5.2.1: Taking the Square Root of Both Sides4

Quadratic Equations A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a 0. Quadratic equations can have no real solutions, one real solution, or two real solutions. When a quadratic has no real solutions, it has two complex solutions. Quadratic equations that contain only a squared term and a constant can be solved by taking the square root of both sides. These equations can be written in the form x2 = c, where c is a constant.5.2.1: Taking the Square Root of Both Sides5Quadratic Equations c tells us the number and type of solutions for the equation.5.2.1: Taking the Square Root of Both Sides6cNumber and type of solutionsNegativeTwo complex solutions0One real, rational solutionPositive and a perfect squareTwo real, rational solutionsPositive and not a perfect squareTwo real, irrational solutionsPractice # 1Solve (x 1)2 + 15 = 1 for x.5.2.1: Taking the Square Root of Both Sides7SolutionIsolate the squared binomial.

Use a square root to isolate the binomial.5.2.1: Taking the Square Root of Both Sides8(x 1)2 + 15 = 1Original equation(x 1)2 = 16Subtract 15 from both sides.

Solution, continuedSimplify the square root. There is a negative number under the radical, so the answer will be a complex number.5.2.1: Taking the Square Root of Both Sides9EquationWrite 16 as a product of a perfect square and 1.Product Property of Square RootsSimplify.

Solution, continuedIsolate x.

The equation (x 1)2 + 15 = 1 has two solutions, 1 4i. 5.2.1: Taking the Square Root of Both Sides10EquationAdd 1 to both sides.

Try This OneSolve 4(x + 3)2 10 = 6 for x.5.2.1: Taking the Square Root of Both Sides11Thanks for Watching!!!!Ms. Dambreville