1. 11.1 Square Roots and Irrational Numbers

2. Perfect Squares
Area of a square
Multiplying a number by itself

3. List of Perfect Squares
1,4,9,16,25,36,49,64,81, 100,121,144,169,196,225…

4. Review: Square root is to find the side lengths of a square given its area

5. .
Square Root -
An operation that yields a number which, when multiplied by itself, produces the given number
Squares
Square Roots

6. Every positive number has two roots.
Positive Square Root
Negative Square Root
(Principal Square Root)
Consider the following:
Two solutions
One solution

7. Simplify each root below and identify as a
positive root or a negative root.

8. Rational vs Irrational
Rational –Anything that can be written as a fraction:
Irrational: Can not be written as a fraction
Perfect Square
Whole Number
Negative Number
Decimal that ends
Decimal that repeats
Fraction
Improper fraction
Mixed number
Square root that does not have a perfect square
A decimal that never ends and never repeats

9. Math Humor

10. Perfect Squares
Rational Roots
Irrational Roots

11. Identify each root as rational or irrational.

12. Estimating Irrational Square Roots
Step 1: Find the two perfect squares the irrational root lies between. (hint use the list of perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100..etc)

13. Determine what two consecutive integers each
irrational root lies between.

14. Estimating Irrational Square Roots
Step 2: Subtract the irrational root from the perfect squares to determine which number it is closest to.

15. Estimate each irrational root to the nearest integer
without using a calculator.

16. Finding the Side of a Square 1) 2)
What would the perimeter be??
1.) 28 un
2.)25.2 un
Distance can’t
be negative

17. Homework
Page 562 (2-38) even