Lesson 2.4 Exercises, pages

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1 Lesson. Exercises, pges A. Expnd nd simplify. ) + b) ( ) () 0 - ( ) () 0 c) -7 + d) (7) ( ) () ( 8). Expnd nd simplify. ) b) ( ) ( ) ( ) 7( 7) 8 (7) P DO NOT COPY.. Multiplying nd Dividing Rdicl Expressions Solutions

2 . Expnd nd simplify. ) + - b) + ( ) ( ) ( ) () ( ) () ( ( )( ) ) ( ) ( ) () ( ) () 9 c) + d) + - ( ( )( ( ) ) ) ( ( ( ) ( ) ) ) ( ( ) ) () ( ) () 0. Rtionlize the denomintor. ) b) () B 7. Expnd nd simplify. ) ( ) 8( ) (7 ) () () 8 7() 8 9 b) ( ( )( 7) 7) ( ( 7) )( ) [ ( ) ( )] () 0 7 [() 0 0 ] Multiplying nd Dividing Rdicl Expressions Solutions DO NOT COPY. P

3 c) ( 7 7( 7) ) ( 7( ) 7 ) 7( 7 ) ( 7) ( 7 )( 7 ) ( ) ( 7 ) (7) 0 7( ) 0 () ( 7) 7( 7) ( ) 9(7) () Identify the vlues of the vrible for which ech expression is defined, then expnd nd simplify. ) w w + The rdicnds cnnot be negtive, so w» 0. w( w ) w( w) w() w w b) x - x + The rdicnds cnnot be negtive, so ( x )( x ) x» 0. x( x ) x( x) ( x ) x() ( x) () x x x 0 x x 0 c) c + d The rdicnds cnnot be negtive, so ( c d) ( c c( d)( c» 0 nd d» 0. c c d) d) d( c d) c cd cd d c cd d d) x - y x + y The rdicnds cnnot be negtive, so x» 0 nd y» 0. The expression is the binomil fctors of difference of squres. ( x y)( x y) ( x) ( y) x 9y P DO NOT COPY.. Multiplying nd Dividing Rdicl Expressions Solutions

4 e) - b - b - - b The rdicnds cnnot be negtive, so» 0 nd b» 0. ( b)( b) ( b) ( ( [ ( ) b) b( ( b) b) b) b( b( ) ( b)( b) b( b) 8 b( b ) b b [ ( b)] ) ( b) b( b)] b b [ b b 9b] b b b b 9b b b 9. Simplify. Describe the strtegy you used in prt c. + ) b) 8 - ( ) 0 ( 8 ) c) d) - 8 In prt c, I first simplified the rdicls, then collected like terms. I ws left with n expression with monomil in the numertor nd in the denomintor. I rtionlized the denomintor, then removed common fctor.. Multiplying nd Dividing Rdicl Expressions Solutions DO NOT COPY. P

5 0. Simplify. - ) b) ( ( 7 ) 7 ) ( 7 ) ( 7) () ( 7) () 7 9 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 7 ( ) ( ) 8 - c) d) Simplify first ( ) ( ) ( ) ( ) ( ) ( ) () ( ) () ( ) () ( ) Rtionlize ech denomintor. Describe ny ptterns in ech list of quotients. Predict the next three quotients in ech pttern. ),,, ( ) 7 ( 7 ) 7 ( ) ( ) ( 7 ) ( 7 ) ( ) ( ) ( ) The numertor of the quotient is the conjugte of the denomintor in the originl expression. The denomintor is the bsolute vlue of the difference of the rdicnds. The next three quotients re: 8 9 0,, 7 8 P DO NOT COPY.. Multiplying nd Dividing Rdicl Expressions Solutions

6 b),,, ( ) ( ) 0 ( ) ( ) ( ) ( ) ( ) ( ) ( ) The first term of the quotient is the squre of the numertor in the originl expression. The second term is the squre root of the product of the rdicnds in the denomintor of the originl expression. The next three quotients re: 0, 7, 8. The dimensions of the Prthenon of ncient Greece re thought to be bsed on the golden rectngle. The length of golden rectngle is times s long s its width. - ) Write the vlue of to deciml plces. - Use clcultor..8 b) Write the vlue of the reciprocl of to deciml plces. - Reciprocl: 0.8 c) Compre the vlues in prts nd b. How re they relted? ; the vlues hve difference of. d) Write n expression to represent the difference between - nd its reciprocl. Simplify the expression. Wht do you notice? A common denomintor is: ( ) () ( ) ( )( ) ( ) ( ) The expression simplifies to, which is the sme s the difference between the estimted deciml vlues in prt c.. Multiplying nd Dividing Rdicl Expressions Solutions DO NOT COPY. P

7 C. ) Simplify. i) - ii) - 8 A common denomintor is: ( ) ( ) 7 Simplify first. 8 A common denomintor is: iii) Rtionlize the denomintor of ech term, then subtrct. 7 ( ( ) ) ( ) ( ( 7 ) 7 ) ( 7 ) Common denomintor: 7 ( 0) (9 ) 7 7( ) b) How re the strtegies you used in prt similr to those used to dd nd subtrct quotients of integers? How re they different? The strtegies re similr in tht I still hve to find common denomintor to dd or subtrct the terms. The strtegies re different in tht I hve to rtionlize the denomintors. P DO NOT COPY.. Multiplying nd Dividing Rdicl Expressions Solutions 7

8 . Rtionlize the denomintor. ) b) To mke the denomintor n integer, I multiply by ( ). ( ) ( ) ( ) To mke the denomintor n integer, I multiply by ( ). ( ) ( ) ( ) x + y. Write, x, y 0 in simplest form. x - y x y ( x y) x y ( ( x y) x y) ( x y) x( x y) y( x y) ( x) ( y) x xy xy y x y x xy y x y. Decide if it is possible to determine two whole numbers nd b tht stisfy ech condition. Justify your nswers. ) b nd re rtionl. b Yes, it is possible. When nd b re perfect squres, b 0, b is product of nturl numbers nd is quotient of nturl b numbers. For exmple, 9, or, nd. 9 b) b nd re irrtionl. b Yes, it is possible. When nd b re different prime numbers, nd re irrtionl. For exmple, b or.9 Á, nd b 0.8 Á. 8. Multiplying nd Dividing Rdicl Expressions Solutions DO NOT COPY. P

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