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Bits,, , | Lo VSG, , Mathematics for Class 8, , , , , , , , 64, , we have:, Solution Writing 3087 as a product of prime factors, 3087 = 3x 3x 7xX7x7. jied by 3., / multip, Clearly, to make it a perfect cube, it must be ne divided so that the, a, EXAMPLEA What is the smallest number by which 392 may, quotient is a perfect cube? wi, ' we a, Solution Writing 392 as a product of prime factors Haut, B92 =2x2x2QKruwe ed by (7 x 7), 1.€-, *9, Clearly, to make ita perfect cube, it must be divid, CUBES OF NEGATIVE INTEGERS, The cube of a negative integer is always negative. pues, EXAMPLES — (-1)° = (-1) x (-1)x(-) =-1, (-2)° =(-2)* (ah, (-3)* = (-3) x (-3) x (-3) = -27, ete., CUBE OF A RATIONAL NUMBER, 3 3, a GQ aA aA AxXaxa — Gi, . 6B bb bo bxbxb b®, 3 3, Hence, (=F) ==., b b®, 3\y 3° ShSx Si am, buss () (5) = Es" 3 cas “8, ay (= * _62)° (2) -2)x(-2) _ =8, 3) 3Smer Saree 27, EXAMPLES. Find the cube of each of the following:, (i) (-7) (ii) 12 (iii) 2.5 (iv) 0.06, Solution We have:, (i) (-7)? = (-7) x (-7) x (-7) = -343., (u) Br see, 3 3 Bro 3x3 Om oa, 3, (iii) (2.5)3 -(3) -(2) DL 5x5x5 ue 125, 10 Ah 25). Ox Does, 6 \3 3 \3 33, (tv) (0.06)R— =) | a2 BOS 27, ie) lea “60)2.” 50 SSgiso ~ jocqan, x50 125000, , PROPERTIES OF CUBES OF NUMBERS, (i) The cube of every even number is even,, (ii) The cube of every odd number ls odd., , a EXERCISE 4A ©, (i) (8)8 (ii) 15)3, , ee ) (15) (iti) (21)3 (iv) (60)°, (i) @,2)3 (ii) (3,5)8 (iii) (0.8)3, , (iv) (0.05)$, , é, , ve, oA Ne!, , a fi’, Pe, Ay *, , SF, |, , }, , |, §, , I, , / zg 48MP Al QUAD:GAMERA, ik Shot by jaat sahab if x ‘ Te, , Lows, ., , ¥, , ImyJa/co/eo, d Ball § =, , , , e, , 4, , “I, , sing, Njb&, , NUN [DS]