Question

A number when divided by 9 leaves a remainder. When the square of the number is divided by 9, the remainder is?

a. 4
b. 3
c. 7
d. 1

Answer 1

When a number is divided by 9, the remainder is considered. When the square of that number is divided by 9, the remainder can be determined by squaring the remainder from the original division. In this case, the remainder is 1.

the correct answer is d. 1.

Step-by-step explanation:

To find the remainder when the square of a number is divided by 9, we need to first find the remainder when the number itself is divided by 9. Let's say the number is x. So x = 9a + remainder, where a is an integer and the remainder is any number less than 9.

When we square x, we get x^2 = (9a + remainder)^2. To find the remainder when x^2 is divided by 9, we can ignore the 9a term because it is divisible by 9. So we are left with (remainder)^2.

Let's consider each of the options:

1. If the remainder is 4, then (4)^2 = 16, and the remainder when 16 is divided by 9 is 7. So option a is not correct.
2. If the remainder is 3, then (3)^2 = 9, and the remainder when 9 is divided by 9 is 0. So option b is not correct.
3. If the remainder is 7, then (7)^2 = 49, and the remainder when 49 is divided by 9 is 4. So option c is not correct.
4. If the remainder is 1, then (1)^2 = 1, and the remainder when 1 is divided by 9 is 1. So option d is correct.