2. Square Roots Tutorial 12c

3. Introduction to Square Roots Just as the inverse of addition is subtraction, and of multiplication is division, the inverse operation of squaring a number is finding a square root. An expression involving a square root such as,, is called a radical expression. The symbol is a radical sign. It indicates the nonnegative or principal square root of the radicand. The radicand is the term or expression inside the radical sign. For Example: In, 81 is the radicand.

4. The square root of 25 is a number that when squared equals 25. 25 = ? 2 ? So, 5 is a square root of 25. Introduction to Square Roots cont... is read “square root of 25”. Try different numbers until you find a number that when squared, it equals 25. 25 = 5 2 25 is 5 squared. ????? 11 2 = 1 22 2 = 4 33 2 = 9 44 2 = 16 55 2 = 25 !

5. Simplifying Square Roots Simplify each expression. Click here to check your answers

6. Simplifying Square Roots Simplify each expression. 6 -8 0 Does not exist positive square root negative square root The square roots are and. There is only one square root of 0. For real numbers, the square root of a negative number is undefined.

7. Estimating & Using Square Roots Estimate by determining what two consecutive integers it lies between. 1st 13 Perfect Squares  1 2 = 1  2 2 = 4  3 2 = 9  4 2 = 16  6 2 = 36  7 2 = 49  8 2 = 64  9 2 = 81  10 2 = 100  11 2 = 121  12 2 = 144  13 2 = 169 To estimate radicals, we must become familiar with perfect squares. Study the table to the left. The numbers on the right side of the table are all perfect squares. 53 is between the two consecutive perfect squares 49 and 64. 7 << 8 Therefore, is between 7 and 8.

8. Estimating & Using Square Roots A calculator can be used to approximate radical expressions. Use a calculator to approximate. cont... Your result should be,  5.57 (rounded to the nearest hundredth) Use a calculator to approximate the following: Round your answers to the nearest hundredth. Click here to check your answers. To find, press,, then. 1 1 3 3

9. Estimating & Using Square Roots A calculator can be used to approximate radical expressions. Use a calculator to approximate. cont... Your result should be,  5.57 (rounded to the nearest hundredth) Use a calculator to approximate the following: Round your answers to the nearest hundredth. To find, press,, then. 1 1 3 3  2.24  11.18  12.65  -4.12  4.69  8.89

10. Using Square Roots to Solve Equations You may recall from a previous unit that a quadratic equation is any equation that can be written in the form: ax 2 + bx + c = 0, where a, b, and c are all real numbers and a  0.  To undo the square, take the square root.  Use a calculator. For Example: Find the value(s) of x that satisfies this equation. Solve 3x 2 – 24 = 0Get x alone on one side. 3x 2 – 24 + 24 = 0 + 24  Add 24 to each side. 3x 2 = 24 x 2 = 8  Divide each side by 3. When b = 0 we have a quadratic that can be solved by using square roots.

11. Using Square Roots to Solve Equations cont... Use square roots to solve each quadratic equation. Round your answers to the nearest hundredth. 1. 5x 2 = 80 2. -10x 2 + 90 = 03. 4x 2 + 18 = 162 Click here to check your answers

12. Using Square Roots to Solve Equations cont... Use square roots to solve each quadratic equation. Round your answers to the nearest hundredth. 1. 5x 2 = 80 2. -10x 2 + 90 = 03. 4x 2 + 18 = 162 x 2 = 16 x =  4 -10x 2 = -90 x 2 = 9 x =  3 4x 2 = 180 x 2 = 45 x   6.71