Mathematics : Squares and Square Roots

Observe 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 = 3^{2
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

Express 49 as the sum of 7 odd numbers.

Express 121 as the sum of 11 odd numbers.

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 27.

Write a Pythagorean triplet whose on member is 15.

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