1.3 – Real Numbers and the Number Line

I.SQUARES and SQUARE ROOTS: The term square root comes from the AREAS of squares and their sides. Because 9 = 3 2, we say that 3 is a SQUARE ROOT of 9

The symbol for theis called the RADICAL. The expression under the radical is the RADICAND. Together they form the SQUARE ROOT. In general, if A = s 2, then s is called a square root of A

Squares and Square Roots you should know: Examples: Simplify the following: 1) 2) 3) 4) x x2x

The square of an integer is a PERFECT SQUARE. To estimate a perfect square, find the two nearest perfect squares and determine which is closer. Estimate the square root. Round to the nearest integer. 1) 2) 3) 4)

II. Sets of numbers A SET is a well defined collection of objects. Each object is called an ELEMENT of the set. A SUBSET of a set consists of elements from the given set. You can list the elements of a set between BRACES: { }

Frequently Used Sets of Numbers Natural Numbers: 1, 2, 3, 4,… Whole Numbers: 0, 1, 2, 3, 4,… Integers: …, -2, -1, 0, 1, 2, … Rational Numbers: … Irrational Numbers: …

Rational Numbers include any terminating or repeating decimal numerals. Rational numbers include any number that can be written in the form where a and b are both integers where

Irrational Numbers include infinite non- repeating decimals. Real numbers include all rational and irrational numbers.

Natural Whole Integers Rational Irrational Real

The square of an integer is a PERFECT SQUARE. To estimate a perfect square, find the two nearest perfect squares and determine which is closer. Name the subset(s) of the real numbers to which each number belongs. 1) 2) 3) 4)

Comparing Real Numbers: An INEQUALITY is a mathematical sentence the compares the values of two expressions using an inequality symbol. Less thanGreater than Less than or equal to Greater than or equal to

Example: Compare the following with an inequality symbol 1) Rewrite as decimal: 2) Compare the decimals: 3) Write using an inequality:

Example: Compare the following using a number line: 1) Rewrite as decimals: 2) Plot on a number line: 3) Write using an inequality:

Homework : TUESDAY: Section 1.3pages #’s 1-8, 10, 14, 16, 17, 20, 22, 23, 26, 29, 33, 37, 41 WEDNESDAY: #’s 13, 19, 25, 29, 34, 40, 42, 46, 48, 60, 65, 66, 67, 68