Question

Q1. Find the square of the following numbers. Using (A + B) 2 = A 2 + 2AB +
B 2
(i) 32
(ii) 86
(iii) 71
(iv) 46

Answer 1

Square of small numbers are easy to find but for large numbers multiplication may prove to be laborious and time consuming.

The method for squaring a two digit number by using the identity

(a+b)²= a²+2ab+b²

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Solution:

1)

32 can be written as (30+2)

 32² = (30+2)²= (30+2)(30+2)

we know the identity

(a+b)²= a² + b² +2ab

 = 30² + 2 x 30 x 2 + 2²

= 900 + 120  + 4 = 1024

(32)² = 1024

2) (35)² = (30+5)²

= 30²+ 2 x 30 x 5  + 5²

= 900 + 300 + 25 = 1225

(35)² =1225

3) 86² = (80 + 6)²

= 80²+ 2 x  80 x 6  + 6²

= 6400 + 960 + 36 = 7396

 86² = 7396

4) 93² = (90+3)²

= 90² +2 x 90 x 3  + 3 ²

= 8100 + 540 + 9 = 8649

93² =  8649

5) 71² = (70 + 1)²

= 70² +2 x 70 x 1  + 1²

= 4900 + 140 + 1 = 5040 + 1 = 5041

 71² =5041

6) 46² = (40+6)²

= 40²+ 2 x 40 x 6  + 6²

= 1600 + 480 + 36 = 2080 + 36 = 2116

 46² =2116

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Hope this will help you...