11.1 and 11.2 Radicals Goal(s): 1.To find the square roots of perfect squares, perfect square radicands and estimate the roots of irrational numbers 2.Determine.

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Presentation transcript:

11.1 and 11.2 Radicals Goal(s): 1.To find the square roots of perfect squares, perfect square radicands and estimate the roots of irrational numbers 2.Determine whether a number is rational or irrational 3.Determine acceptable replacements for radicands

Square Roots When we raise a number to the second power, we have “squared” the number. Sometimes we need to find the number that was squared. That process is called “finding the square root of a number”. Every positive number has both positive and negative square roots. Radical Sign “Principal” Square Root is the positive 5.

Simplify: (Answer is only the principal root) 9 -8 Negative square Root Because (9) 2 = 81 (6) 2  -36 (-6) 2  -36 Not possible

Perfect Square Radicands

Simplify:

Comes from the word “ratio” Any number that can be expressed as the ratio of two integers Rational Numbers

Ir rational Numbers Cannot be written as the ratio of two integers. Decimal never ends and does not repeat. Examples of irrational numbers: 

Identify the number as irrational or rational The square roots of most whole numbers are irrational. Only the perfect squares (0, 1, 4, 9, 16, 25, 36, etc.) have rational square roots.

Identify the rational number:

Real Numbers: All the rational and all the Irrational numbers. Real Numbers Rational Numbers Irrational Numbers

Approximate the value of

Find without a calculator: 15

Find without a calculator: 17

Radical Expressions (an expression written under a radical) Radicand (the expression written under the radical) The radicand must be positive!

Evaluate the expression for x = 5. Is the result a real number?

Evaluate the expression for x = 2. Is the result a real number?

Determine the values of x that make the expression a real number.

Homework Work book Page 38 ( 2-32) even