Lesson 11-1 Square Roots and Irrational Numbers 3 1 2 112 242 392 The square of an integer is a perfect square. The opposite of squaring a number is taking the square root. Example For example 81 asks what number multiplied by itself is equal to 81? That number is 9. Is there another solution to that problem? Example For example 81 asks what number multiplied by itself is equal to 81? That number is 9. Is there another solution to that problem? Yes, -9 is also a solution. Simplify each square root 100 16 Simplify each square root 100 10 16 Simplify each square root 100 10 16 -4 Squares and roots Here is a list that will be helpful: 112 11 242 42 392 93 42 16 16 4 52 25 25 5 62 36 36 6 72 49 49 7 82 64 64 8 92 81 81 9 102 100 100 10 112 121 121 11 122 144 144 12 Do you see that squares and square roots are inverses (opposites) of each other? Estimating square roots Once we have memorized these squares and their roots, we can estimate square roots that are not perfect squares For example, what about 8 ? Estimating square roots We find the two perfect squares that are before and after the square root of 8. and 9 Look at them on a number line: 2 3 4 5 6 7 8 2 3 Estimating square roots We can see that 8 is between 2 and 3 but is closer to 3. We would say that 8 is approximately 3.9 2 3 4 5 6 7 8 2 3 TRY THIS: Estimate to the nearest whole number 27 78 50 TRY THIS: Estimate to the nearest whole number 27 5 78 50 TRY THIS: Estimate to the nearest whole number 27 5 78 -9 50 TRY THIS: Estimate to the nearest whole number 27 5 78 -9 50 7 Rational number- can be written as a fraction Irrational number- cannot be written as a fraction because: • it is a non-terminating decimal • it is a decimal that does NOT repeat * The square roots of ALL perfect squares are rational. * The square roots of numbers that are NOT perfect squares are irrational. Try This: Identify each number as rational or irrational 2 81 0.53 0.627 13.875931... Try This: Identify each number as rational or irrational 2 Irrational 81 0.53 0.627 13.875931... Try This: Identify each number as rational or irrational 2 Irrational 81 Rational 0.53 0.627 13.875931... Try This: Identify each number as rational or irrational 2 Irrational 81 Rational 0.53 Rational 0.627 13.875931... Try This: Identify each number as rational or irrational 2 Irrational 81 Rational 0.53 Rational 0.627 Rational 13.875931... Try This: Identify each number as rational or irrational 2 Irrational 81 Rational 0.53 Rational 0.627 Rational 13.875931... Irrational.