Squaring two-digit numbers
Squaring of two-digit numbers is quite easy if we work near base numbers. Let us find the square of a number near a base, i.e. numbers that are near 10, 100, 1000 etc. We have already seen how to find the square of numbers greater than the base numbers. Today we will find the square of numbers that are less than the base numbers.
Example: Find the square of 96
●The base is 100.
●96 is 4 less than the base. Let us call that the deficient.
●Subtract the the deficient from the given number: 96 – 4 = 92. That is the first part of the answer.
●Square the deficient, which gives the second part of the answer. 42 = 16.
Answer: 9216
We have to be clear about the number of digits in the second part of the answer. Since the base is 100, which has two zeroes, we need to have two digits in the second part of the answer.
Let us look at a problem with fewer digits than the base.
Find the square of 98
●The base is 100. The deficient is 2.
●First step: 98 – 2 = 96.
●Second step: 22 = 4. Because the base is 100 we need two digits in the second part of the answer or the answer will be wrong.
●So we make it 04.
●The final answer is 9604
We may also get a situation when we have more digits than the number of zeros in the base.
Example: Find the square of 88
●The base is 100, and the deficient is 12.
●88 – 12 = 76, the first part of the answer.
●122 = 144, the second part of the answer.
●But we know only two digits are allowed in the second part of the answer. So put 44 in the answer and carry over the 1 to the hundreds place. 76 becomes 77.
●So the answer is 7744
In all problems that involve the base the number of digits needs to be the same as the number of zeroes in the base.
Now you can try,
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