How can you find the dimensions of a square or a circle when you are given its area? When you multiply a number by itself, you square the number.

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1 7. Finding Squae Root How can you find the dimenion of a quae o a cicle when you ae given it aea? When you multiply a numbe by itelf, you quae the numbe. Symbol fo quaing i the exponent. = = 6 quaed i 6. To undo thi, take the quae oot of the numbe. Symbol fo quae oot i a adical ign,. 6 = = The quae oot of 6 i. ACTIVITY: Finding Squae Root Wok with a patne. Ue a quae oot ymbol to wite the ide length of the quae. Then find the quae oot. Check you anwe by multiplying. a. Sample: = = ft Aea ft Check The ide length of the quae i feet. 0 b. Aea 8 yd c. Aea cm d. Aea 6 mi Squae Root In thi leon, you will find quae oot of pefect quae. evaluate expeion involving quae oot. ue quae oot to olve equation. e. Aea 5 mi f. Aea.89 in. g. Aea ft 9 88 Chapte 7 Real Numbe and the Pythagoean Theoem

2 ACTIVITY: Uing Squae Root Wok with a patne. Find the adiu of each cicle. a. b. Aea 6 in. Aea yd c. d. Aea 0.5 ft 9 Aea m 6 ACTIVITY: The Peiod of a Pendulum V I D E O Math Pactice Calculate Accuately How can you ue the gaph to help you detemine whethe you calculated the value of T coectly? Wok with a patne. The peiod of a pendulum i the time (in econd) it take the pendulum to wing back and foth. The peiod T i epeented by T =. L, whee L i the length of the pendulum (in feet). Copy and complete the table. Then gaph the function. I the function linea? L T L. IN YOUR OWN WORDS How can you find the dimenion of a quae o a cicle when you ae given it aea? Give an example of each. How can you check you anwe? Ue what you leaned about finding quae oot to complete Execie 6 on page 9. Section 7. Finding Squae Root 89

3 7. Leon Leon Tutoial Key Vocabulay quae oot, p. 90 pefect quae, p. 90 adical ign, p. 90 adicand, p. 90 A quae oot of a numbe i a numbe that, when multiplied by itelf, equal the given numbe. Evey poitive numbe ha a poitive and a negative quae oot. A pefect quae i a numbe with intege a it quae oot. Finding Squae Root of a Pefect Squae Study Tip Zeo ha one quae oot, which i 0. Find the two quae oot of = 9 and ( 7) ( 7) = 9 So, the quae oot of 9 ae 7 and 7. The ymbol i called a adical ign. It i ued to epeent a quae oot. The numbe unde the adical ign i called the adicand. Poitive Squae Root, Negative Squae Root, Both Squae Root, ± 6 = 6 = ± 6 = ± Finding Squae Root Find the quae oot(). a. 5 Becaue 5 = 5, 5 = 5 = 5. 5 epeent the poitive quae oot. b. 9 6 Becaue ( ) = 9 6, 9 6 ( = ) =. 9 epeent the 6 negative quae oot. c. ±.5 ±.5 epeent both the poitive and the negative quae oot. Becaue.5 =.5, ±.5 = ±.5 =.5 and.5. Execie 7 8 Find the two quae oot of the numbe Find the quae oot().. 5. ± Chapte 7 Real Numbe and the Pythagoean Theoem

4 Squaing a poitive numbe and finding a quae oot ae invee opeation. You can ue thi elationhip to evaluate expeion and olve equation involving quae. Evaluating Expeion Involving Squae Root Evaluate each expeion. a = 5(6) + 7 Evaluate the quae oot. = Multiply. = 7 Add. b. + 8 = + 9 Simplify. = + Evaluate the quae oot. = Add. c. ( 8 ) 5 = 8 5 Evaluate the powe uing invee opeation. = 76 Subtact. Real-Life Application The aea of a cop cicle i 5,6 quae feet. What i the adiu of the cop cicle? Ue. fo π. A = π Wite the fomula fo the aea of a cicle. 5,6. Subtitute 5,6 fo A and. fo π.,00 = Divide each ide by..,00 = Take poitive quae oot of each ide. 0 = Simplify. The adiu of the cop cicle i about 0 feet. Execie 0 7 Evaluate the expeion ( ) 0. The aea of a cicle i 86 quae feet. Wite and olve an equation to find the adiu of the cicle. Ue. fo π. Section 7. Finding Squae Root 9

5 7. Execie Help with Homewok. VOCABULARY I 6 a pefect quae? Explain.. REASONING Can the quae of an intege be a negative numbe? Explain.. NUMBER SENSE Doe 56 epeent the poitive quae oot of 56, the negative quae oot of 56, o both? Explain. 9+(-6)= +(-)= +(-9)= 9+(-)= Find the dimenion of the quae o cicle. Check you anwe.. Aea cm 5. Aea.69 km 6. Aea 6 in. Find the two quae oot of the numbe Find the quae oot() ± 96. ± ± ERROR ANALYSIS Decibe and coect the eo in finding the quae oot. Evaluate the expeion. 0. ( 9 ) ( ) ( 5 ) ( ± = + ) 8. NOTEPAD The aea of the bae of a quae notepad i.5 quae inche. What i the length of one ide of the bae of the notepad? 9. CRITICAL THINKING Thee ae two quae oot of 5. Why i thee only one anwe fo the adiu of the button? A 5 mm 9 Chapte 7 Real Numbe and the Pythagoean Theoem

6 Copy and complete the tatement with <, >, o = SAILBOAT The aea of a ail i 0 quae feet. The bae and the height of the ail ae equal. What i the height of the ail (in feet)?. REASONING I the poduct of two pefect quae alway a pefect quae? Explain you eaoning. h 5. ENERGY The kinetic enegy K (in joule) of a falling apple i epeented by K = v, whee v i the peed of the apple (in mete pe econd). How fat i the apple taveling when the kinetic enegy i joule? b Aea cm 6. PRECISION The aea of the two watch face have a atio of 6 : 5. a. What i the atio of the adiu of the malle watch face to the adiu of the lage watch face? b. What i the adiu of the lage watch face? 7. WINDOW The cot C (in dolla) of making a quae window with a ide length of n inche i epeented by C = n A window cot $55. What i 5 the length (in feet) of the window? 8. The aea of the tiangle i epeented by the fomula A = ( )( 7)( 0), whee i equal to half the peimete. What i the height of the tiangle? 7 cm cm 0 cm Wite in lope-intecept fom an equation of the line that pae though the given point. (Section.7) 9. (, ), (5, ) 0. (, 7), (, ). ( 5, ), (5, ). MULTIPLE CHOICE What i the value of x? (Section.) A B C 88 D (x 8) 8 x Section 7. Finding Squae Root 9