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Sunday 2nd of October Home Square Roots and Radical Expressions Solving Radical Equations Simplifying Radical Expressions Irrational Numbers in General and Square Roots in Particular Roots of Polynomials Simplifying Radical Expressions Exponents and Radicals Products and Quotients Involving Radicals Roots of Quadratic Equations Radical Expressions Radicals and Rational Exponents Find Square Roots and Compare Real Numbers Radicals Radicals and Rational Exponents Theorems on the Roots of Polynomial Equations SYNTHETIC DIVISION AND BOUNDS ON ROOTS Simplifying Radical Expressions Exponents and Radicals Properties of Exponents and Square Roots Solving Radical Equations Rational Exponents and Radicals,Rationalizing Denominators Rational Exponents and Radicals,Rationalizing Denominators Quadratic Roots Exponents and Roots Multiplying Radical Expressions Exponents and Radicals Solving Radical Equations Solving Quadratic Equations by Factoring and Extracting Roots Newton's Method for Finding Roots Roots of Quadratic Equations Studio Roots, Radicals, and Root Functions Review division factoring and Root Finding Radicals Simplifying Radical Expressions Multiplying and Simplifying Radical Expressions LIKE RADICALS Multiplication and Division of Radicals Radical Equations BOUNDING ROOTS OF POLYNOMIALS
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# Find Square Roots and Compare Real Numbers

Goal • Find square roots and compare real numbers.

 VOCABULARY Square root If b^2=a, then b is a square root of a. Square roots are written with the radical symbol . Radicand The number or expression inside the radical symbol Perfect square A number whose square roots are integers Irrational number A number that cannot be written as the quotient of two integers Real number The set of all rational and irrational numbers
 SQUARE ROOT OF A REAL NUMBER Words If b^2=a, then b is a square root of a . Example 5^2 = 25 and (-5)^2 = 25, so 5 and -5 are square roots of 25.

Example 1 Find square roots

 All positive real numbers have two square roots, a positive and a negative square root. The positive square root is called the principal square root. Evaluate the expression. Solution The negative square root of 36 is 26 .The positive square root of 16 is 4 The positive and negative square roots of 64 are 8 and 28 .

Guided Practice Evaluate the expression. Example 2 Classify numbers

Tell whether each of the following numbers is a real number, a rational number, an irrational number, an
integer, or a whole number: Solution

 Number Real Number ? Rational Number? Irrational Number ? Integer ? Whole Number ? Yes Yes No Yes Yes Yes Yes No Yes No Yes No Yes No No

Example 3 Graph and order real numbers

Order the numbers from least to greatest: Solution
Begin by graphing the numbers on a number line. Read the numbers from left to right: Guided Practice Complete the following exercises.

3. Tell whether each of the following numbers is a real number, rational number, irrational number, integer,
or whole number: Real number: Rational number: Irrational number: Integer: Whole number: Homework

4. Order the numbers from Exercise 3 from least to greatest. 