Which one among , , , has last digit 4?

Question

Homi · Accepted Answer

Understand the Question

The last digit (unit digit) of the square of any number depends only on the square of its unit digit.
If a number has unit digit $u$ , then the unit digit of its square is the unit digit of $u^2$ .
Numbers ending in $2$ or $8$ have squares that end in $4$ , because $2^2 = 4$ and $8^2 = 64$ .

Step 1 · Find the Last Digit of $64^2$

The unit digit of $64$ is $4$ .

$4^2 = 16$

Therefore, the last digit of $64^2$ is $6$ .

Step 2 · Find the Last Digit of $108^2$

The unit digit of $108$ is $8$ .

$8^2 = 64$

Therefore, the last digit of $108^2$ is $4$ .

Step 3 · Find the Last Digit of $292^2$

The unit digit of $292$ is $2$ .

$2^2 = 4$

Therefore, the last digit of $292^2$ is $4$ .

Step 4 · Find the Last Digit of $36^2$

The unit digit of $36$ is $6$ .

$6^2 = 36$

Therefore, the last digit of $36^2$ is $6$ .

Answer

$108^2$ and $292^2$

Common Mistakes

Computing the Full Square: Calculating long multiplications like $292 \times 292$ instead of just squaring the unit digit ( $2^2 = 4$ ).
Missing One of the Values: Overlooking that both numbers ending in $2$ and $8$ yield a square ending in $4$ ( $2^2 = 4$ and $8^2 = 64$ ), leading to naming only one instead of both $108^2$ and $292^2$ .

Question 2