Question

Which of the following numbers will have 6 at their unit place:
(A) $ {26^2} $
(B) $ {49^2} $
(C) $ {34^2} $
(D) $ {43^2} $

Answer 1

Hint: Use the concept, the unit place of the product of any tow numbers is the unit place of the product of the unit places of those numbers. You can verify this concept by taking simple examples. And then use it to find which options conform this concept.

Complete step-by-step answer:
Observe the concept:
The unit place of the product of any two numbers is the unit place of the product of the unit places of those numbers.
For example, let us take two numbers 2 and 16
Then the product of these two numbers is $ 2 \times 16 = 32 $ .
The unit place digit is 2.
Now, use the concept we stated, for that, we will take the unit place digits of both the numbers and multiply them. It would be, $ 2 \times 6 = 12 $
This is a two-digit number. The concept explains that, in such a case, we can take the unit place digit of the number that we get.
Hence, the unit place digit of the product of the given two numbers is 2.
We can clearly observe that the answer after multiplying the digits directly and the answer after using the concept we have stated above is the same.
So, now, by using the same concept, we can say that the unit place digit in
Option (A) $ = 6 \times 6 = 36 \to 6 $
Option (B) $ = 9 \times 9 = 81 \to 1 $
Option (C) $ = 4 \times 4 = 16 \to 6 $
Option (D) $ = 3 \times 3 = 9 \to 9 $
Therefore, from the above explanation, the correct answer is, option (A) $ {26^2} $ and option (C) $ {34^2} $
So, the correct answer is “Option A AND C”.

Note: We can always use multiplication of digits directly to find the term in the unit place. But that would be difficult. Like in this example, calculating the squares of all these large terms would have been little difficult in comparison to the concept that we used.