Question

Find \[1397 \times 1397 = ?\]
A.1951609
B.1981709
C.18362619
D.2031719
E.None of these

Answer 1

Hint: The product mentioned above looks difficult but it is not at all difficult. We will write the given number as such a firm that will help us to solve it easily. That is we will write the number as \[1397 = 1400 - 3\] . Now this will be taken two times since the given number is a product of the same number. So we will then expand the bracket using the algebraic identity \[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\] .

Complete step by step solution:
Given that,
 \[1397 \times 1397 = ?\]
We can write \[1397 = 1400 - 3\]
Now the question changes to,
 \[ = \left( {1400 - 3} \right)\left( {1400 - 3} \right)\]
Taking the simplified form,
 \[ = {\left( {1400 - 3} \right)^2}\]
Now comparing this with \[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\] we can write
 \[ = {\left( {1400} \right)^2} - 2 \times 1400 \times 3 + {3^2}\]
Taking the squares and the product,
 \[ = 1960000 - 8400 + 9\]
On rearranging the terms,
 \[ = 1960009 - 8400\]
And on solving we get,
 \[ = 1951609\]
This is the answer.
So, the correct answer is “Option A”.

Note: Note that don’t tick any answer at random. These types of questions are just tricky. Sometimes we can choose the answer just from some logic. Like here the same number is multiplied to the same number so the units place digit must be a digit that is on square of 7. But unfortunately, here all options have 9 on the unit's place. Then go for the method mentioned above. We can simply eliminate the option C because it has 8 digits whereas the answer is only 7 digit long.