www.Guide4BankExams.blogspot.in Square & Squareroots multipl ied by itself then the pr oduct is the square of the number. Thus the square of 5 is 5x5 Square : If a number is multiplied = 25 2
1 1 1 1 eg. x 2 2 2 4 2
2 2 4 2 x 3 3 3 9
r oot of a number is one of two equal factors which is mul multiplied tiplied together gives tha t Square root: The square root number. eg. Ö121 = Ö11x11 = 11 Ö10000 = Ö100 x 100 = 100 Finding Square root by means of factorisation
When a given number is a per fect square, we resolve resolve it into prime factors and take tak e the product of prime factors, choosing one out of each pair. eg. Find the square squar e root of 1156 Factors of 1156 is 2x2x17x17 1156=2x2x17x17=22x17 x172 Ö1156 = Ö22 x 172 = 2x17 = 34 General Genera l method to find the square root
In the given number mark off the digits in pairs, from right and then find the square root as shown shown in the example exampl e below. below. eg. 1.Find 1. Find the square root of 219961 469 4 21,99,61 16 86 599 516 929 8361 8361 0 Ö219961 = 469 2.
Find Find the the squa square re roo roott of of 59.1 59.136 3611 7
7.69 59.1361 49
146 1529
1013 876 13761 13761 0
Ö59.1361 = 7.69 Properties of a perfect square
¨
No perfe rfect squa quare ends nds with 2,3 2,3,,7,8
¨
No pe perfe rfect squ squar aree end endss wit withh an odd odd num numbe berr of of ze zeros. ros.
www.Guide4BankExams.blogspot.in ¨
The The per perfe fect ct squa square re co consist nsistin ingg of of (n-1 (n-1)) or or n dig digit itss will will have have n 2 digits in their r oot
¨
The squa square re of of a numb number er othe otherr than unity unity is eit either her a mult multip iple le of of 4 or or exce exceed edss a multi multiple ple of 4 by 1.
CUBE ROOT
The cube root of a number is one of three equal factors whi ch if multiplied gives gi ves that number. Cube root of a number can be found out by using the following steps. 1. Write down down all the prime prime fact factors ors of the given given numbe numbers. rs. 2. Write the prime prime facto factors rs in the the index index notati notation, on, ie, in an form. 3. Divide Divide the index by by 3, then then the result result will will be the cube cube root root of the given given number. number. eg. 1. Find the th e cube root of of 512 512=(2x2x2) x (2x2x2) x (2x2x2) 3
9 13 3 51 2 = (2 ) 2 8
2. Find the th e cube root root of 0.000027 3 13
13
27 3 . 3. 0000027 1000000
=
3
3 13
100
3 0.03 100 10 0
Learn by heart the following square roots SQUARES AND CUBES
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Squar e
Cube
1 4 9 16 25 36 49 64 81 100 121 144 169 196 225
1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375
No
Square
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Ö2= 1. 1.41421 Ö3= 1.73205
Ö6 =2 =2.44949 Ö7 = 2.6 2.644575
Ö5=2.2360
Ö10 = 3.1622
256 289 324 361 400 441 484 529 576 625 676 729 784 841 900
PRACTICETEST
1.
If x = Ö301 Ö30188 + Ö36 Ö36+Ö +Ö16 169, 9, the value value of x is is a) 44 b) 55 55 c) 69 d) 43
2.
If x =
3.
1. 6 9x 0.9 1. 3x0.1 3
, the value of x is
a)
3
b) 13 13
c) 39
If
x 4 , the value of x x is 49 7
d) 0.39
www.Guide4BankExams.blogspot.in a) 4.
7
12
5 8
a)
6.
d) 15
324 x 0.4 ? 9
b)
8 5
c)
100 10000
9 5
d)
10 5
b) 1000 d) 1,00,000
a)
26 26
c) 8
101.82 d) 36 Ö? + 44 = 25% of 400
a)
3
If x = a)
10.
c) 8
14 4 32 4 10 4 x ? 6 6 16 9
7.
9.
d) 4
169 16 . 9 , the value of x is If x
a) c)
8.
b) 10 10
484 x 11
5.
c) 16 16
1 96 18 65 the value of x is 7 32 4 16 9
If x = a)
b) 49
b) 14
b) 36 36
c) 49 49
d) 16
81 , the value of x is 0.0 9
3
b) 30 30
c) 300
d) 0.3
The largest largest of four four digit number numberss which which is a perfec perfectt squre squre is a)
9801
b) 99 9904
c)
9804
d) 98 9809
11. A certain number number of people people collecte collectedd Rs. 125. 125. If each each person contributed contributed as many many five five paise as they they are in number, the number of person person were a) 25 b) 50 c) 100 d) 125 12. A gardener plants an orchard with with 5776 trees. trees. In each each row there were were as many trees as the number of rows. rows. Find the number num ber of rows. rows. a) 76 b) 96 96 c) 66 d) 186 13. Each student student in a class contributed contributed as many rupees as the number number of studnets in the class for a picnic. The school contributed Rs. 150 per teacher who led the trip. If the total am ount collected was Rs. Rs. 1350 and th e number of teachers who led the trip was 3, how many students were there in that class? a) 36 b) 35 35 c) 34 d) 30 14. Some persons contributed contributed Rs. Rs. 1089. Each Each person gave gave as many many rupees as they are in number. Find their number. a) 33 b) 66 66 c) 45 d) 23 15.
If 1 a)
16. 16.
0
x 13 then x is equal to. 144 12
b) 12 12
1 69 4 9 22 5
c) 13 13 81 1 21
?
d) 25
www.Guide4BankExams.blogspot.in 9 55
a)
7 5
17. 17.
7 5
a) c) 18.
19.
b)
11 45
c) 4
1 45 d) 11 11
is equal to b) 6 3 5 d) 1
6 35 2
If 0.04 x 0.4 xa = 0.004 x 0.4 x b , a)
16x10-4
b)
16x10-3
c)
16x10-5
d)
16x10-6
then
a is b
1 1 1 is 2 1 3 2 2 3
The value lue of of (a) -1
b) 0
c) 1
1 1 d) 3 2 3
20.
The value lue of 4 0 0 1 6 8 1 is a) 41 b) 21 21 c) 31 d) 51
21.
if 5 2.2 4 and a)
1.37
b) 1.57
6 2.4 5 , the value of
c) 1.73
2 5 is 3 6
d) 1. 1.75
22.
If 1 56 5 6 2 5 1 25 2 5 then the value of 1 5 6 2 5 1 5 6.2 5 1.5 6 2 5 is a) 1.3875 b) 13.875 c) 138.75 d) 156.25
23.
If 4 0 9 6 = 64 to then the value of 4096 . 040 0409 . 96 000 00 . 04096 000 0000 . 004096
is a) c) 24.
25. 25.
26.
d)
b) 7. 7.1014 7.12 2
The The exp expre resssio sion a)
2
c)
2 2
2
1 2
2
1 2 2
equals
b) 2 2 d) 2 2
3 1 5 . 5 4 27 27 is equal to
a)
12 3
c)
3 3
b) 9 3 d) 3
If 5 2.24 2 4 then the value of a) c)
27.
7.09 7.1104
0.168 16.8
3 5 2 5 0.4 8
is
b) 1. 1.68 d) 16 168.0
Supp Suppoose you know know that that 1 5 is approximately 3.88 which of the following is the best approximation to a) 0.43 b) 1.89
5 ? 3
www.Guide4BankExams.blogspot.in c) 28.
1.29
If 1 3.69 69 0.60 6 0 2 5 x 3 7.2 5 then x is equal to a)
10
b) 100
441 x 3
2 25 x 5
a)
21
b) 28 28
4 x
3
a)
8
c)
8
29. 29.
30. 30.
31.
2 4 3 81
2 3
c) 1000 d) 11 1125 64 256
?
c) 48 27 3
d) 84 20
x
5
b) 8
1 4
d) 8
3 4
equals
3 2 If 6 2.4 5 then the value of correct upto three thre e places of decimals is 3 2
a) c) 32.
d) 1.63
1.000 0.100
b) 0. 0.990 d) 0. 0.101
If 8 6 when approximated appr oximated to one place of decimal decimal is 9.3 then the value of
43 upto one place of decimal 2
is
33.
34.
a)
18.6
b) 4.63
c)
4.6
d) 4.636
If 1 8 22 th e value of 18225 182.25 2 2 5 1 35 3 5 , then the 2 5 1.8225 0.0 18 182 25 is a)
1.49985
b)
14.9985
c)
149.985
d)
1499.85
3 2 3 If 6 2.4 5 then the value of equals 3 2 3
a) c) 35.
0.41 4.10
b) 0.42 d) 4.20
The The squ squar aree ro root of of
0 .3 2 4 x 0 .0 8 1 x 4.6 2 4 1.5 6 25 2 5 x 0 .0 28 2 8 9 x 7 2.9 x 6 4 is
a)
24.0
b) 2.4
c)
0.24
d) 0. 0.024
www.Guide4BankExams.blogspot.in ANSWERS TO PRACTICE TEST
1.
(b)
2.
(a)
3.
(c)
9.
(b)
10. (a)
11. (b)
17. (a)
18. (c)
25. (c) 33. (c)
4.
(c)
5. (b)
6.
(c)
7.
(a)
8.
(c)
12. (a)
13. (d)
14. (a)
15. (d)
16.(b)
19. (c)
20. (b)
21.(c)
22. (c)
23. (c)
24. (a)
26. (b)
27. (c)
28. (d)
29.(d)
30. (c)
31. (c)
32.(c)
34. (b)
35. (d)
