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Taking the Square Root of Both Sides

Taking the Square Root of Both Sides. Adapted from Walch Education. Complex Numbers. The 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.

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Taking the Square Root of Both Sides

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  1. Taking the Square Root of Both Sides Adapted from Walch Education

  2. Complex Numbers • The imaginary unit irepresents the non-real value . iis the number whose square is –1. We define iso that and i2 = –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 iis the imaginary unit. 5.2.1: Taking the Square Root of Both Sides

  3. Real Numbers • Real 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 Sides

  4. Irrational Numbers • Real 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 π. 5.2.1: Taking the Square Root of Both Sides

  5. 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 Sides

  6. Quadratic Equations c tells us the number and type of solutions for the equation. 5.2.1: Taking the Square Root of Both Sides

  7. Practice # 1 Solve(x – 1)2 + 15 = –1 for x. 5.2.1: Taking the Square Root of Both Sides

  8. Solution Isolate the squared binomial. Use a square root to isolate the binomial. 5.2.1: Taking the Square Root of Both Sides

  9. Solution, continued Simplify 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 Sides

  10. Solution, continued Isolate x. The equation (x – 1)2 + 15 = –1 has two solutions, 1 ± 4i. 5.2.1: Taking the Square Root of Both Sides

  11. Try This One… Solve4(x + 3)2 – 10 = –6 for x. 5.2.1: Taking the Square Root of Both Sides

  12. Thanks for Watching!!!! Ms. Dambreville

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