Finding the Last Digit of a Product and its Square

To find the last digit of a large number resulting from multiplication and squaring, we only need to focus on the last digits of the numbers involved in the calculation.

Step 1: Find the last digit of the product (1068 × 486 × 928)

The last digit of a product is determined solely by the product of the last digits of the numbers being multiplied.

• The last digit of 1068 is 8.
• The last digit of 486 is 6.
• The last digit of 928 is 8.

Now, let's multiply these last digits:

\(8 \times 6 \times 8\)

First, multiply \(8 \times 6\):

\(8 \times 6 = 48\)

The last digit of 48 is 8.

Next, multiply the last digit of 48 (which is 8) by the last digit of 928 (which is 8):

\(8 \times 8 = 64\)

The last digit of 64 is 4.

So, the product (1068 × 486 × 928) ends in the digit 4.

Step 2: Find the last digit of the square of the product

The question asks for the last digit of \((1068 \times 486 \times 928)^2\). We know that the product \((1068 \times 486 \times 928)\) ends in the digit 4.

To find the last digit of a number squared, we only need to square its last digit.

The last digit of the product is 4. We need to find the last digit of \(4^2\).

\(4^2 = 4 \times 4 = 16\)

The last digit of 16 is 6.

Conclusion

Therefore, the number \((1068 \times 486 \times 928)^2\) will end in the digit 6.

Let's check the options:

The calculated last digit is 6, which matches option 4.