Section 2.7 square roots (algebra)
- 1. Section 2.7 Square Roots and Real Numbers
- 2. By definition 25 is the number you would multiply times itself to get 25 for an answer. Because we are familiar with multiplication, we know that 25 = 5 Numbers like 25, which have whole numbers for their square roots, are called perfect squares
- 3. Perfect square Square root 1 1 = 1 4 4 = 2 9 9 = 3 16 16 = 4 25 25 = 5 36 36 = 6 49 49 = 7 64 64 = 8 81 81 = 9 100 100 = 10 121 121 = 11 144 144 = 12 169 169 = 13 196 196 = 14 225 225 = 15 Perfect square Square root
- 4. Every whole number has a square root Most numbers are not perfect squares, and so their square roots are not whole numbers. Most numbers that are not perfect squares have square roots that are irrational numbers Irrational numbers can be represented by decimals that do not terminate and do not repeat Rational + Irrational = REAL Numbers
- 5. Obj: To find the square root of a number Find the square roots of the given numbers If the number is not a perfect square, use a calculator to find the answer correct to the nearest thousandth. 81 37 158 81 = 9 37 6.083 158 12.570
- 6. Obj: To find the square root of a number Find two consecutive whole numbers that the given square root is between Try to do this without using the table 18 115 18 is between 4 and 5 115 is between 10 and 11 16 = 4 and 25 = 5 so 100 = 10 and 121 = 11 so
- 7. Obj: To find the square root of a number Find two consecutive whole numbers that the given square root is between Try to do this without using the table 29 73 29 is between 5 and 6 73 is between 8 and 9 25 = 5 and 36 = 6 so 64 = 8 and 81 = 9 so
- 8. Obj: To find the square root of a number Find two consecutive whole numbers that the given square root is between Try to do this without using the table 150 55 150 is between 12 and 13 55 is between 7 and 8 144 = 12 and 169 = 13 so 49 = 7 and 64 = 8 so
- 9. Simplify the following expressions = 4 81 2 9 4 81 = 1 36 1 144 – = 1 6 1 12 – = 2 12 1 12 – = 1 12
- 10. Graphing real numbers The graph of a number is a dot placed where the number would be on the number line 0 5 10 -5 -10 Graph the number: 3 1 2 0 5 10 -5 -10 Graph the number: -8.5