radical symbol 1 Use a Calculator to Find Square Roots 2 Find Side Lengths

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1 Page 1 of Simplifying Square Roots Goal Simplify square roots. Key Words radial radiand Square roots are written with a radial symbol m. An epression written with a radial symbol is alled a radial epression, or radial. The number or epression inside the radial symbol is the radiand. radial symbol 2 5 radial radiand The radial symbol always indiates the nonnegative square root of a number. For eample, beause Find the square root of 52. Round your answer to the nearest tenth. Chek that your answer is reasonable. 1 Use a Calulator to Find Square Roots Calulator keystrokes Display Rounded value 52 or This is reasonable, beause 52 is between the perfet squares 49 and 64. So, 5 2 should be between 4 9 and 6 4, or 7 and 8. The answer 7.2 is between 7 and 8. STUDY TIP Reall that for any number a 0, ( a ) 2 a. Use the Pythagorean Theorem to find the length of the hypotenuse to the nearest tenth. 2 Find Side Lengths a 2 b 2 2 Write Pythagorean Theorem. ( 2 ) 2 ( 3 ) 2 2 Substitute 2 for a and 3 for b Simplify. 5 2 Add. 5 Take the square root of eah side. 2.2 Use a alulator Simplifying Square Roots 537

2 Page 2 of 5 SKILLS REVIEW To review the Produt Property of Radials, see p Multiplying Radials You an use the Produt Property of Radials to multiply radial epressions. a p b a b, where a 0 and b 0. 3 Multiply Radials Multiply the radials. Then simplify if possible. a. 3 p 7 b. 2 p 8 a. 3 p 7 3 p 7 b. 2 p 8 2 p Simplifying Radials You an also use the Produt Property of Radials to simplify radial epressions. a b a p b, where a 0 and b 0. To fator the radiand, look for perfet square fators. 4 Simplify Radials Simplify the radial epression. STUDY TIP When you fator a radiand, write the perfet square fators first. a. 1 2 b. 4 5 a p 3 b p 5 4 p 3 9 p Find the square root. Round your answer to the nearest tenth. Chek that your answer is reasonable Multiply the radials. Then simplify if possible p p p p 3 Simplify the radial epression. 538 Chapter 10 Right Triangles and Trigonometry Evaluate, Multiply, and Simplify Radials

3 Page 3 of Eerises Guided Pratie Voabulary Chek 1. What is the radiand in the epression 2 5? Math the radial epression with its simplified form A p 2 B p 6 C. 4 2 Skill Chek D. 6 Use the figure shown at the right. 6. Use the Pythagorean Theorem to find the length of the hypotenuse in radial form. 7. Use a alulator to find the length of the hypotenuse to the nearest tenth. 2 4 Simplify the epression Pratie and Appliations Etra Pratie See p Finding Square Roots Find the square root. Round your answer to the nearest tenth. Chek that your answer is reasonable Pythagorean Theorem Find the length of the hypotenuse. Write your answer in radial form Homework Help Eample 1: Es Eample 2: Es Eample 3: Es Eample 4: Es Pythagorean Theorem Find the missing side length of the right triangle. Round your answer to the nearest tenth Simplifying Square Roots 539

4 Page 4 of 5 Multiplying Radials Multiply the radials. Then simplify if possible p p p p p p 2 2 Square a Radial Evaluate the epression. a. (3 7 ) 2 b. (2 1 1 ) 2 a. (3 7 ) p3 7 b. (2 1 1 ) p p3p 7 p 7 2p2p 1 1 p 1 1 9p7 4p Squaring Radials Evaluate the epression. Use the eample above as a model. 32. (6 5 ) (5 3 ) (7 2 ) 2 Simplifying Radials Simplify the radial epression You be the Judge Determine whether the epression an be simplified further. If so, eplain how you would do so p p p p p 2 p 4 p Area Formula Use the area formula A lw to find the area of the retangle. Round your answer to the nearest tenth. I I C L A S S Z O N E. C O M HOMEWORK HELP Etra help with problem solving in Es is at lasszone.om Chapter 10 Right Triangles and Trigonometry

5 Page 5 of Area of an Equilateral Triangle The area of an equilateral triangle with side length s is given by the formula A 1 4 s 2 3. The flower bed shown is an equilateral triangle with a side length of 30 feet. Find its area. 30 ft 30 ft 30 ft 53. Challenge An equilateral triangle has an area of 1 square meter. What is the length of eah side? Round your answer to the nearest entimeter. Standardized Test Pratie 54. Multiple Choie Whih number is a perfet square? A 44 B 110 C 169 D Multiple Choie is between whih two integers? F 12 and 13 G 13 and 14 H 14 and 15 J 15 and Multiple Choie Whih of the following epressions ould not be used to represent the length of the hypotenuse in the triangle shown at the right? A B C about 10.2 D Mied Review Finding Angle Measures Find the measure of a1. (Lesson 4.2) Isoseles Triangles Find the value of. (Lesson 4.3) Algebra Skills Distributive Property Use the distributive property to rewrite the epression without parentheses. (Skills Review, p. 671) 63. ( 5) 64. 4(2 1) 65. (3 4) 66. 5( 2) 67. 3(1 ) ( 6) 10.1 Simplifying Square Roots 541