Short Answer TypeObserve the following pattern and supply the missing number.
112 = 121
1012 = 10201
101012 = 102030201
10101012 = ........................
...........2 = 102030405030201
Using the given pattern, find the missing numbers.
12+22 +22 = 32
22+32 +22 = 62
32+42 +122 = 132
42+52 +___2 = 212
52+__2 +302 = 312
62+72+___2 =_____2
Note: To find pattern:
Third number is related to first and second number. How?
Fourth number is related to third number. How?
Without adding, find the sum.
(i) 1 + 3 + 5+ 7+ 9
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
How many numbers lie between squares of the following numbers?
(i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100
Find the square of the following numbers containing 5 in unit’s place.
(i) 15 (ii) 95 (iii) 105 (iv) 205
Find the square of the following numbers.
(i) 32 (ii) 35 (iii) 86
(iv) 93 (v) 71 (vi) 46
(i) (32)2 = (30 + 2)2
= 302 + 2(30)(2)+(2)2
= 900 + 120 + 4
= 1024
(i) (35)2 = (30 + 5)2
= 302 + 2(30)(5)+(5)2
= 900 + 300 + 25
= 1225
Second method
(35)2 = 3 x (3 + 1) x 100 + 25
= 3 x 4 x 100 + 25
= 1200 + 25
= 1225\
(iii) (86)2 = (80 + 6)2
= (80)2 + 2(80)(6)+(6)2
= 6400 + 960 + 9
= 8649
(iv) (93)2 = (90 + 3)2
= (90)2 + 2(90)(3)+(3)2
= 8100 + 540 + 9
= 8649
(v) (71)2 = (70 + 1)2
= (70)2 + 2(70)(1)+(1)2
= 4900 + 140 + 1
= 5041
(vi) (46)2 = (40 + 6)2
= (40)2 + 2(40)(6)+(6)2
= 1600 + 480 + 36
= 2116
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