EasyExam

1. A certain number of persons agree to subscribe as many rupees each as there are subscribers. The whole subscription is Rs.2582449. Find the number of subscriber? Let the number of subscribers be x, say since each subscriber agrees to subscribe x rupees. The total subscription = no. of persons × subscription per person = x × x = x 2 X 2 =2582449 ∴ x = 1607 2. Simplify: 3√ 192 a 3 b 4 Use the 2 formulas (abc) m =a m b m c m (a m ) n =a mn 3√192a 3 b 4 =(192a 3 b 4 ) 1/3                 =(192) 1/3 .(a 3 ) 1/3 (b 4 ) 1/3                 =(2 6 x3).ab 4/3                 =2 2. 3 1/3 .ab 4/3                 =4a.(3b 4 ) 1/3                 =4a. 3 √3b 4 3.simplify 3√x 9 y 12           Solution:3√x 9 y 12 =(x 9 y 12 ) 1/3                                              =(x 9 ) 1/3 (y 12 ) 1/3                                                    =x 3 y 4   4.Find the number whose square is equal to the difference between the squares of 75.12 and

THEORY OF INDICES 1.a m xa n =a m+n 2.(a m ) n =a mn 3.a m /a n =a m-n 4.(ab) m =a m b m 5.a 0 =1 6.a x/y =y th root of a x = y √a x 7.a 1/p =p th root of a 8.(ab/c) m =a m b m /c m 9.a ∞ =∞ 10.a -∞ =0 Find the least number with which you multiply 882, so that the product may be a perfect square. First find the factors of 882. 882 = 2 × 3 × 3 × 7 × 7 Now, 882 has factors as shown above, ‘3’ repeated twice, ‘7’ repeated twice and ‘2’ only once. So when one more factor ‘2’ is used, then it becomes a perfect square. 882 × 2 = (2 × 2) × (3 × 3) × (7 × 7) The least number required is ‘2’

Characteristics of square roots of numbers 1.If a square number ends in ‘9’, its square root is a number ending in’3’ or ‘7’. 2. If a square number ends in ‘1’, its square root is a number ending in’1’ or ‘9’. 3. If a square number ends in ‘5’, its square root is a number ending in’5’ 4. If a square number ends in ‘4’, its square root is a number ending in’2’ or ‘8’. 5. If a square number ends in ‘6’, its square root is a number ending in’4’ or ‘6’. 6. If a square number ends in ‘0’, its square root is a number ending in ‘0’ Ex: 1)√529=23    √729=27    √1089=33   √ 1369=37, etc 2)√121= 11    √361= 19    √961 =31      √81= 9,etc 3)√625=25 √1225=35 √2025=45 & so on 4)√484=22     √64=8    √1024=32    √784=28 & so on 5)√196=14     √256=16    √576=24    √676=26 & so on 6)√100=10     √400=20    √10000=100 & so on