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.
2 3 4 5 6 7 8 9
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