Mini-Lecture 8.1 Introduction to Radicals

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1 Copyright 01 Pearson Education, Inc. Mini-Lecture 8.1 Introduction to Radicals 1. Find square roots.. Find cube roots.. Find nth roots.. Approimate square roots.. Simplify radicals containing variables. Eamples: 1. Find each square root f) 0.. Find each cube root Find each root Approimate each square root to three decimal places Find each root. Assume that all variables represent positive numbers. a 8 m yz f) 9 7a bc Many students confuse 1, 1, and. Students have a hard time understanding even though we assume that all variable represent positive numbers. It is very important to stress that using a calculator gives an approimation and leaving an answer in radical form is an eact value. Answers: 1 7; 1 1/; 1 -; 1 not a real number; 1 /11; 1f) 0.8; ; -; -/; ; -; -/;.;.9; -10.9; ; a ; m ; 9 ; yz ; f) a bc M-1

2 Copyright 01 Pearson Education, Inc. Mini-Lecture 8. Simplifying Radicals 1. Use the product rule to simplify square roots.. Use the quotient rule to simplify square roots.. Simplify radicals containing variables.. Simplify higher roots.. Key Vocabulary: perfect squares. Eamples: 1. Use the product rule to simplify each radical f) 0. Use the quotient rule and the product rule to simplify each radical Simplify each radical. Assume that all variables represent positive numbers. 9 y 1 a 18 y f) 1 80y g) 98 p h) 00 0 i) 1 10 z. Simplify each radical Many students have trouble with radicals. When simplifying, students get confused where to write the numbers outside the radical symbol or in the radicand. A common error is to evaluate 1. Many students do not know when to stop! Each section in the tet has worksheets in the Etra Practice featuring differentiated learning. Answers: 1 ; 1 ; 1 ; 1 10 ; 1 0; 1f) 1 ; /; 1 ; ; 10 h) ; i) 10 z ; y y ; ; a a ; 00 ; ; y y ; f) M- y ; g) 11 ; 7 ; p

3 Copyright 01 Pearson Education, Inc. Mini-Lecture 8. Adding and Subtracting Radicals 1. Add or subtract like radicals.. Simplify radical epressions, and then add or subtract any like radicals. Eamples: 1. Add or subtract as indicated Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables represent positive numbers f) 8. Simplify each radical epression f) 7 Many students need etra practice in identifying like radicals. Some students combine the coefficients and multiply the like radicals. Many students confuse and. In fact, a common error is to evaluate or. Encourage students to be cautious determining the inde. Each section in the tet has worksheets in the Etra Practice featuring differentiated learning. Answers: 1 ; ; ; 1 ; ; ; 8 ; ; ; 8 ; f) ; 8 7 ; 0 ; 1 ; f) ; 1 10; M-

4 Copyright 01 Pearson Education, Inc. Mini-Lecture 8. Multiplying and Dividing Radicals 1. Multiply radicals.. Divide radicals.. Rationalize denominators.. Rationalize using conjugates.. Key Vocabulary: product rule for radicals, quotient rule for radicals, rationalizing, conjugates. Eamples: 1. Multiply and simplify. Assume that all variables represent positive real numbers. f) 1 g) 7 7 h) 8 99 i) 8. Divide and simplify. Assume that all variables represent positive real numbers y y. Rationalize each denominator and simplify. Assume that all variables represent positive real numbers Rationalize each denominator and simplify. Assume that all variables represent positive real numbers. 7 1 Many students have trouble with problem 1i. They tend to square each term in the binomial rather than squaring the binomial. Most students are able to rationalize a denominator with one term. Many students have difficulty rationalizing a denominator with terms. Each section in the tet has worksheets in the Etra Practice featuring differentiated learning. Answers: 1 1 ; 1 ; 1 ; 1 9 ; 1 ; 1f) ; 1g) -; 1h) ; 1i) 11 ; ; ; y; ; 1 ; ; 1 1 ; 7 1; 9 M-

5 Copyright 01 Pearson Education, Inc. Mini-Lecture 8. Solving Equations Containing Radicals 1. Solve radical equations by using the squaring property of equality once.. Solve radical equations by using the squaring property of equality twice. Eamples: 1. Solve each equation y 11 f) y9 y g) 1 h) 8 i) 9 0. Solve each equation Mied Practice. Solve each equation. 1 7 f) 11 9 Many students have to be reminded to isolate the radical before squaring both sides. Refer students to the tetbook for To Solve a Radical Equation Containing Square Roots. Many students find the concept of etraneous solutions confusing. Show students a simple eample of an etraneous solution, such as: square both sides is etraneous. Each section in the tet has worksheets in the Etra Practice featuring differentiated learning. Answers: 1 ; 1 ; 1 ; 1 not real; 1 9; 1f) 0; 1g) 1; 1h) 1; 1i) ; ; ; ; ; 8; f) M-