Question

Can you please tell me the formula for finding squares between 25 and 75. Can you also please tell the formula for finding squares between 75 and 125

Answer 1

TO CALCULATE SQUARES FROM 25 TO 50

Let us use one formula:

(25+x) ^2= (25-x) ^2+100x ----------------- (1)

Example: calculate Square of 28.

Solution: let us solve this using equation 1.

28^2= (25+3) ^2= (25-3) ^2+100.3=22^2+300=484+300=784

Example: calculate Square of 31.

Solution: let us solve this using equation 1.

31^2= (25+6) ^2= (25-6) ^2+100.6=19^2+600=361+600=961

Example: calculate Square of 38.

Solution: let us solve this using equation 1.

38^2= (25+13) ^2= (25-13) ^2+100.13=12^2+1300=144+1300=1444.

SQUARES FROM 50 TO 75

(50+x)^2= x^2+2500+100x

eq. calculate square of 57

57^2= (50+7) ^2=7^2+2500+100.7=49+2500+700=3249

Note: Last two digit of a (50+x) ^2 will be same as last two digit of x^2.

Example: calculate Square of 68.

68^2= (50+18) ^2=18^2+2500+100.18=324+2500+1800=4624.

SQUARE FROM 76 TO 125

100+x)^2 = (100 + 2x).100 + x^2

Observe above expression:

Last two digits= same as last two digits of x^2

Remaining Digits= (100 + 2x)

Example: calculate square of 124.

Solution: 124^2= (100+24) ^2;

24^2=576

Last two digits= last two digits of 24^2 = 76 & carry=5

Remaining digits= (100+2.24) + carry

= 148+5

=153

So, 124^2= 15376

Example: calculate square of 112.

112^2= (100+12) ^2

12^2=144

Last two digits= last two digits of 12^2 = 44 & carry=1

Remaining digits= (100+2.12) + carry

= 124+1

=125

So, 112^2= 12544