1. Rational and Irrational Numbers
Square Roots and
Rational and Irrational Numbers

3. The square of an integer is a perfect square.3 2 1
The square of an integer is a perfect square.
The opposite of squaring a number is taking the square root.

4. Example
For example
asks what number multiplied by itself is equal to 81? That number is 9.
Is there another solution to that problem?

5. Example
For example
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.

6. Simplify each square root

7. Simplify each square root10

8. Simplify each square root10 -4

9. Squares and roots
Here is a list that will be helpful:

10. Do you see that squares and square roots are inverses (opposites) of each other?

11. 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 ?

12. Estimating square roots
We find the two perfect squares that are before and after the square root of
and
Look at them on a number line: 2 3

13. Estimating square roots
We can see that is between 2 and 3 but
is closer to 3. We would say that is approximately 3. 2 3

14. TRY THIS: Estimate to the nearest whole number

15. TRY THIS: Estimate to the nearest whole number5

16. TRY THIS: Estimate to the nearest whole number5 -9

17. TRY THIS: Estimate to the nearest whole number5 -9 7

18. Rational vs. Irrational Numbers

19. Rational number- can be written as a fraction of two integers
Irrational number- cannot be written as a fraction of two integers 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.

20. Key Things to Remember:
The sum or product of a rational number is rational.
The sum of a rational number and irrational number is irrational.
The product of a nonzero rational number and an irrational number is irrational.

21. Try This: Identify each number as rational or irrational

22. Try This: Identify each number as rational or irrational

23. Try This: Identify each number as rational or irrational

24. Try This: Identify each number as rational or irrational

25. Try This: Identify each number as rational or irrational

26. Try This: Identify each number as rational or irrational