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The formula used for finding squares ending in 5 is "by one more than the one before".
The answer comes in two parts
LHS and RHS.
LHS is computed by multiplying the digit before 5 by the digit one more
than that,
i.e. by its next consecutive digit.
RHS is always 25 as the number ends in 5, and we know that 52 = 25.
Let us understand it better with the following example:
Example 1: Find the square of 35
LHS = The digit before 5 (i.e. 3) is multiplied by its next consecutive digit 4, i.e. 3×4 = 12
RHS = as the number ends in 5, so
52 = 25
So, the final answer for 35^{2} is
352 = 1225
Example 2: Find the square of 75
LHS = 7 × 8 = 56
RHS = 52 = 25
So, the final answer for 75^{2} is 5625
Let's understand it better with the following example:
Example 1: Multiply 25 by 11
Write 2 & 5 of 25 as it is and the sum of 2 & 5 (i.e. 7) in between.
So, 25 × 11 = 275
Similarly, 71 × 11 = 781 (sum of 7 & 1, i.e. 8 in between)
Example 2: Multiply 42631 by 11
In longer calculations like this, we first write the border numbers, i.e.
4 & 1 as it is and then
write the sum of next successive pairs in between as shown below:
4 & 1 as it is, as two border numbers. Then, starting from the left side,
we keep writing the sum of the two digits:
4+2= 6, 2+6= 8, 6+3= 9, 3+1=4
So, the final answer for 75^{2} is 5625
Example 3: Multiply 4573 by 11
0+3 = 3
7 + 3 = _{1}0 (1 is carried to the next step)
5 + 7 = 12
12 + 1 (carry) = _{1}3 (1 is carried to the next step)
4 + 5 = 9
9 + 1 (carry) = _{1}0 (1 is carried to the next step)
0 + 4 = 4
4 + 1 (carry) = 5 (1 is carried to the next step)
So, the answer of 4573 × 11 is 50303
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