This is an adaptation of the previous post Square of numbers close to powers of 10

Lets take some examples 389 , 77 , 416

Step 1:

Difference = 389-400=-11

Step 2:

Square of difference = 121 This is the right side ,but 1 is carried to the left side.

So now right hand side becomes 21 with carry 1.

Step 3:

Add 389 and -11 = 378

Multiply this with 4(because 4*100= 400 ie. 4 times a power of 10)

378*4 = 1512

This is the left side.But now we need to add the carry from right side 1.

So 1512+1=1513

Answer 389

Step1:

Difference =316-300=16

Step2:

Square of 16=256

So right side is 56 with carry 2.

Step 3:

316+16=332

332*3=996

Add the carry 2 to 996 = 998

Answer 316

Step1:

Difference = 77-80=-3

Step2:Square of -3 = 9

Right side =9

Step3:

77-3=74

74*8=544

Left side =592

Answer 77

Lets take some examples 389 , 77 , 416

**389**is near to 400.Step 1:

Difference = 389-400=-11

Step 2:

Square of difference = 121 This is the right side ,but 1 is carried to the left side.

So now right hand side becomes 21 with carry 1.

Step 3:

Add 389 and -11 = 378

Multiply this with 4(because 4*100= 400 ie. 4 times a power of 10)

378*4 = 1512

This is the left side.But now we need to add the carry from right side 1.

So 1512+1=1513

Answer 389

^{2}= 151321**316**is near to 300Step1:

Difference =316-300=16

Step2:

Square of 16=256

So right side is 56 with carry 2.

Step 3:

316+16=332

332*3=996

Add the carry 2 to 996 = 998

Answer 316

^{2}= 99856**77**is near to 80Step1:

Difference = 77-80=-3

Step2:Square of -3 = 9

Right side =9

Step3:

77-3=74

74*8=544

Left side =592

Answer 77

^{2}= 5929