Last week we discussed the squaring of numbers with 5 as the units digit. Now we will look at a method to find the square if the number is near a base. Let us recollect the steps:
If a number is less than the base, subtract the decrement to the number to get the first part of the answer and then square the decrement to get the second part of the answer.
If the number is greater than the base then add the increment to the number to get the first part of the answer and square the increment to get the second part of the answer.
Numbers higher than the base
Let us find the square of 106
Answer: 11236
Numbers lower than the base
Let us find 932
Answer: 8649
Square of any two-digit number.
This has three simple steps.
1. Square the tens digit.
2. Multiply 2 x first digit x second digit.
3. Square the units digit.
Combine the parts to get the answer.
Example: 342
32 = 9
2 x 3 x 4 = 24
42 = 16
Combine the parts, carrying over where required. The 1 of 16 is carried over to 24, giving 25. The 2 of 25 is carried over to 9, giving 11.
9 24 16
11 5 6
Answer: 1156
682
1. 62 = 36
2 x 6 x 8 = 96
82 = 64
The 6 of 64 is carried over to 96, giving 102. The 10 of 102 is carried over to 36, giving 46.
36 96 64
36 102 4
46 2 4
Answer: 4624
Tip of this week: Decide the method depending on the question.