Question

A number, when divided by 5 leaves, remainder 2. when the square of the number is divided by 5, the remainder will be: 4 b 2 c 1 3

Answer 1

If the number divided by 5 leaves remainder 2, then let the number be 5x + 2.

Squaring 5x + 2,

(5x + 2)²

= 25x² + 20x + 4

= 5 (5x² + 4x) + 4

∴ The square of the number divided by 5 leaves remainder 4.

4 is the answer.

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Answer 2

Given,

A number, when divided by 5, leaves the remainder 2

To find,

When the square of a number is divided by 5, its remainder

Solution,

Let the number be 'a'

On dividing this number by 5 we get the remainder of 2

So, the number would be 5a + 2

Now, for calculating the remainder of the square of a number, multiplying the number by itself:

-> (5a+2)^2

-> 25a^2 + 10a +10a + 4

-> 25a^2 + 20a + 4

Dividing the number by 5

-> (25a^2+20a+4)/5

-> [5(5a^2+4a) + 4]/5

-> 5a^2 + 4a + 4/5

It will give the remainder of 4

Hence, when the square of a number is divided by 5, its remainder will be 4