Warm UpSimplify:

7² =

3.5² =

15² =

0.4² =

49

12.25

225

0.16

Chapter 11, Section 1

Square Roots and Irrational Numbers

By Ms. Dewey-Hoffman

Area of a Square

The area of a square is the SQUARE of the length of a side. (s²)

The square of an integer is a perfect square.

Example: 2² = 4 (4 is a perfect square)4² = 16 (16 is a perfect square)

Everything in Math has an Opposite

The opposite of a SQUARE is a SQUARE ROOT.

The symbol: √ indicates a NONNEGATIVE Square Root of a number.Square Root = Radical

Same thing!!!

Examples

Simplify each Square Root:

√64 = ?

-√121 = ?

√100 = ?

-√16 = ?

8

-11

10

-4

13 Perfect Squares

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, and 144.

Recommend Memorizing.

Estimating Non-Perfect Squares

For Integers that are NOT perfect squares, you can estimate a square root.

√4 √9

2 2.5 3

√8 = 2.83

Estimating Square Roots to the Nearest Integer.

√15 → Look for the two perfect squares on either side of 15.

√9 < √15 < √16 → 15 is closer to 16.

√16 = 4Square root of 15 is close to 4.

√15 ≈ 4√15 = 3.87...

Estimate to the Nearest Integer

√27 =

-√72 =

√50 =

-√22 =

5

-8

7

-5

Classifying Real Numbers

RATIONAL Numbers as the RATIO of two integers: decimals and fractions.

But the decimal either repeats or terminates.

IRRATIONAL Numbers CANNOT be expressed as a ratio and NEITHER repeat nor terminate.

Positive Integer not a Perfect Square?Then the square root is irrational.

Identifying Rational or Irrational√18 = irrational, 18 not a perfect square

√121 = rational, 121 is a perfect square

-√24 = irrational, 24 not a perfect square

432.8 = rational, terminating decimal

0.1212... = rational, repeating decimal

0.120120012... = irrational

π = irrational

Identify Each

√2 = rational or irrational

-√81 = rational or irrational

0.53 = rational or irrational

√42 = rational or irrational

Assignment #30

Pages 562-563:

2-34 even #s, 39-45 all.