Are You Ready? Simplify Radical Expressions

Transcription

1 SKILL Are You Read? Simplif Radical Epressions Teaching Skill Objective Simplif radical epressions. Review with students the definition of simplest form. Ask: Is written in simplest form? (No) Wh or wh not? ( is a perfect square factor.) Is 7 written in simplest form? (No, because there is a fraction under the radical sign.) Is written in simplest form? (Yes, even though there is a fraction, the denominator does not have a radical in it.) Net, review with students how to simplif radical epressions. Work through each eample. Point out that when the epression involves a product or a fraction, it ma be more convenient to multipl or divide first, then simplif. Provide the following eample:. Ask: Is or a perfect square? (No) If ou multipl first, do ou get a perfect square inside the radical? (Yes, ) Provide a similar eample using a fraction (e.g. ). Have students complete the eercises. PRACTICE ON YOUR OWN In eercises 8, students simplif radical epressions. CHECK Determine that students know how to simplif radical epressions. Students who successfull complete the and are read to move on to the net skill. COMMON ERRORS Students ma leave a radical epression in the denominator of a fraction. Students who made more than errors in the, or who were not successful in the section, ma benefit from the Alternative Teaching Strateg. Alternative Teaching Strateg Objective Simplif radical epressions. Some students ma benefit from seeing the connection between square roots and squares more directl. Remind students that the first step in simplifing a radical is to check for perfect squares. If the number inside the radical is the square of an integer, it can be simplified. Write the following problem on the board: Ask: Since taking the square root of a number is the inverse of squaring the number, what can be said about the square root of a number squared? (It is equal to the number.) Have students complete the following table. n n n n Write the problems below on the board. Have students rewrite the problems as n and then simplif. Remind students that if the epression is a product, the can simplif each term separatel and then multipl. Likewise, if the epression is a fraction, the can simplif the numerator and the denominator one at a time. 6 ; 8 ; 6 6 6,, Holt McDougal Geometr

2 Name Date Class SKILL Are You Read? Simplif Radical Epressions Definition: A radical epression is in simplest form when all of the following conditions are met.. The number, or epression, under the radical sign contains no perfect square factors (other than ).. The epression under the radical sign does not contain a fraction.. If the epression is a fraction, the denominator does not contain a radical epression. How to Simplif Radical Epressions Look for perfect square factors and simplif these first. If the radical epression is preceded b a negative sign, then the answer is negative. Eample : Simplif 8. Since 8 is a perfect square factor, simplif the epression to. 8 8 If the epression is a product, simplif then multipl, or multipl then simplif, whichever is most convenient. Eample : Simplif 6. Since both numbers are perfect squares, simplif then multipl: If the epression is (or contains) a fraction, simplif then divide, or divide then simplif, whichever is most convenient. Eample : Simplif Simplif each epression () Simplif each epression Holt McDougal Geometr

3 SKILL 77 Are You Read? Solve Proportions Teaching Skill 77 Objective Solve proportions. Review with students the definition of a proportion. Point out that ou can also think of a proportion as two equivalent fractions. Ask: If two fractions are equivalent, what is true about their simplest forms? (The are equal.) Write two equivalent fractions on the board, such as. Ask: Is this a true statement and wh? (Yes, because the fractions are equivalent.) Tell students that this is a proportion. Show students b pointing what the cross products of this proportion are. ( and ) Ask: What is true about the cross products? (The are equal.) Eplain to students that this is the ke to solving proportions. Review with students the steps for solving a proportion. Then work through the eample. Remind students that it does not matter which side the variable is on when solving an equation. PRACTICE ON YOUR OWN In eercises, students solve proportions. CHECK Determine that students know how to solve proportions. Students who successfull complete the and are read to move on to the net skill. COMMON ERRORS Students ma multipl the numerators together and the denominators together, rather than finding the cross products. Students who made more than errors in the, or who were not successful in the section, ma benefit from the Alternative Teaching Strateg. Alternative Teaching Strateg Objective Solve proportions. Tell students that it is possible in man proportions to follow a pattern to solve the proportion. Write the following proportion on the board: 6. Ask: If ou look at the 6 8 numerators, what are ou multipling b to get from to 6? () What are ou multipling b in the denominators to get from 6 to 8? () Write the following on the board: Eplain that because ou are multipling both the numerator and the denominator b the same number, ou still have equivalent ratios since. Write the following on the board: 6 8 Have students find the value of b multipling 6 times. () Tell students that this process also works if ou are dividing the numerator and denominator b the same number. Write the following on the board: 7 8. Have students draw a diagram of the division, like the multiplication diagrams above. ( on each piece; answer: ) Have students use this technique to solve the following proportions: 8 ; ; 7 ; 77 8 ; 8 6 ; and ( ; ; ; 6; ; 6) Then have students solve problems with in the numerator. 6 Holt McDougal Geometr

4 Name Date Class SKILL 77 Are You Read? Solve Proportions Definition: A proportion is an equation that shows two equivalent ratios. Ke propert: The cross products of a proportion are equal. To solve a proportion, follow these two steps: Step : Find the cross products. Step : Simplif if necessar and solve the equation for the variable. Eample: Solve 6 Step : Find the cross products. Step : Simplif and solve Multipl. 6 8 Divide both sides b 6. 8 Solve each proportion Solve each proportion Holt McDougal Geometr

5 Name Date Class CHAPTER 7 Enrichment Angles and More Angles A perfect number is a number which is the sum of its own positive factors (other than itself). For eample, the following numbers are perfect What is the net perfect number? To discover the answer, find the value of in each figure. Then, cross out the answer in the bo at the bottom of the page. The sum of all the remaining angles is the net perfect number Holt McDougal Geometr

6 Answer Ke continued SKILL ANSWERS: SKILL ANSWERS: SKILL ANSWERS: Holt McDougal Geometr

7 Answer Ke continued SKILL 76 ANSWERS:. perpendicular. parallel. perpendicular. neither. parallel 6. neither 7. perpendicular 8. perpendicular. perpendicular. perpendicular. parallel. parallel. parallel. neither. perpendicular SKILL 77 ANSWERS: SKILL 78 ANSWERS: Holt McDougal Geometr