Evaluating Square Roots Chapter 9 Section 1

Learning Objective Evaluate Square Roots of real numbers Recognize that not all square roots represents real numbers Determine whether the square root of a real number is rational or irrational Write square roots as exponential expressions

Key Vocabulary square root root principal square root imaginary radical sign radicand radical expression index root imaginary perfect square perfect square factor rational number irrational number

Evaluate Square Roots of Real Numbers positive or principal square root uses the to indicate a positive square root if “The square root of a” Negative square roots are indicated by

Evaluate Square Roots of Real Numbers radical sign is radicand is the number under the radical sign radical expression is the entire expression Index tells the root of the expression and the squared root index are not written All squares of a nonzero real number must be positive

Evaluate Square Roots of Real Numbers square root is the reverse process of squaring a number Example : because 72 = (7)(7) = 49 The is 0, written

Evaluate Square Roots of Real Numbers Examples:

Evaluate Square Roots of Real Numbers Examples:

Negative Square Roots Negative square roots are not real numbers How do we know that the square of any nonzero real number must be a positive number? Example:

Perfect Squares The numbers 1, 4, 9, 16, 25, 36, 49, … are perfect squares because each number is a square of a natural number. See page 536 for a list of the first 20 perfect squares. Natural numbers 1 2 3 4 5 Square Natural number 12 22 32 42 52 Perfect squares 1 4 9 16 25

Rational Numbers A rational number can be written as a and b are integers and b ≠ 0 Rational numbers written as a decimal are either terminating or repeating. ½ = .5 or ⅓ = .333… Round you answers two decimal place and use the approximately equal sign ≈

Rational Numbers The square root of every perfect square is also a rational number.

Irrational Numbers A irrational number is any number that is not rational and are non-terminating and non-repeating decimals. The square root of non perfect square are irrational number

Writing a Square Root in Exponential Form Reviewing the rules for exponents in chapter 4 section 1 and 2 may be helpful.

Writing a Square Root in Exponential Form

Review of Rules for Exponents Product Rule: Quotient Rule: Zero Exponent Rule:

Review of Rules for Exponents Power Rule: Expanded Power Rule: Negative Exponent Rule:

Remember The square root is the opposite or reverse process of squaring. “Square of a number” “Multiply the number by itself” Every real number greater than 0 has two squares one positive and one negative Square roots of negative numbers are not real numbers. They are imaginary numbers

Remember The results of a square root is always nonnegative. The result is only rational if the radicand is a perfect square The radical form is the exact value. Calculators only give approximate values for irrational numbers. We use the ≈ sign for these values.

Remember You should try to memorize as many perfect squares as possible to help with simplifying in the next section. Review of factoring may also be helpful for simplifying in the next section. Extra practice may be helpful to remember the difference between and

HOMEWORK 9.1 Page 539 - 540 # 13, 21, 23, 31, 33, 37, 41, 65, 71, 74