Which one among , , , has last digit 4?

Question

Homi · Accepted Answer

To find the last digit of a square number, we only need to look at the last digit of the original number.

Step 1 — Finding the last digit of a square

The last digit of a number's square is determined by the last digit of the number itself. Let us consider an example.

Let the number be $N$ . Let its unit's digit be $u$ . The unit's digit of $N^2$ will be the unit's digit of $u^2$ .

For example, for $12^2$ : The unit's digit of 12 is 2. We square this unit's digit: $2^2 = 4$ . So, the last digit of $12^2$ (which is $144$ ) is 4.

Step 2 — Checking $64^2$

Let us find the last digit of $64^2$ . The unit's digit of 64 is 4.

We square this unit's digit: $4^2$ $= 16$ The last digit of $16$ is 6.

$\boxed{\text{The last digit of } 64^2 \text{ is } 6.}$

Step 3 — Checking $108^2$

Next, let us find the last digit of $108^2$ . The unit's digit of 108 is 8.

We square this unit's digit: $8^2$ $= 64$ The last digit of $64$ is 4.

$\boxed{\text{The last digit of } 108^2 \text{ is } 4.}$

Step 4 — Checking $292^2$

Now, let us find the last digit of $292^2$ . The unit's digit of 292 is 2.

We square this unit's digit: $2^2$ $= 4$ The last digit of $4$ is 4.

$\boxed{\text{The last digit of } 292^2 \text{ is } 4.}$

Step 5 — Checking $36^2$

Finally, let us find the last digit of $36^2$ . The unit's digit of 36 is 6.

We square this unit's digit: $6^2$ $= 36$ The last digit of $36$ is 6.

$\boxed{\text{The last digit of } 36^2 \text{ is } 6.}$

Answer

(i) The last digit of $64^2$ is 6. (ii) The last digit of $108^2$ is 4. (iii) The last digit of $292^2$ is 4. (iv) The last digit of $36^2$ is 6. The numbers whose squares have a last digit of 4 are $108^2$ and $292^2$ .

Question 2

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