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When we divide a number say x by 6 it leaves a remainder 3. When we divide the square of the same number by 6, what will be the remainder?
- a)0
- b)3
- c)6
- d)9
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
When we divide a number say x by 6 it leaves a remainder 3. When we di...
Let x = 6q + 3.
Then, x2 = (6q + 3)2
= 36q2 + 36q + 9
= 6(6q2 + 6q + 1) + 3
Thus, when x2 is divided by 6, then remainder = 3.
Then, x2 = (6q + 3)2
= 36q2 + 36q + 9
= 6(6q2 + 6q + 1) + 3
Thus, when x2 is divided by 6, then remainder = 3.
Most Upvoted Answer
When we divide a number say x by 6 it leaves a remainder 3. When we di...
Understanding the Problem:
When a number x is divided by 6, it leaves a remainder of 3. We need to find out the remainder when the square of the same number is divided by 6.
Solution:
To find the remainder when the square of a number is divided by 6, we need to first understand the concept of remainders when numbers are divided by 6.
Remainder when a number is divided by 6:
- When a number x is divided by 6, it leaves a remainder of 3. This can be represented as x = 6q + 3, where q is the quotient.
- The possible remainders when a number is divided by 6 are 0, 1, 2, 3, 4, or 5.
Finding the Remainder when the Square of the Number is divided by 6:
- Let's consider the number x as 6q + 3, where q is the quotient.
- The square of x can be represented as (6q + 3)^2 = 36q^2 + 36q + 9.
- On simplifying, we get (36q^2 + 36q + 9) = 6(6q^2 + 6q) + 3.
- This shows that when the square of a number x is divided by 6, it leaves a remainder of 3.
Therefore, the remainder when the square of a number is divided by 6 is 3, which corresponds to option 'B'.
When a number x is divided by 6, it leaves a remainder of 3. We need to find out the remainder when the square of the same number is divided by 6.
Solution:
To find the remainder when the square of a number is divided by 6, we need to first understand the concept of remainders when numbers are divided by 6.
Remainder when a number is divided by 6:
- When a number x is divided by 6, it leaves a remainder of 3. This can be represented as x = 6q + 3, where q is the quotient.
- The possible remainders when a number is divided by 6 are 0, 1, 2, 3, 4, or 5.
Finding the Remainder when the Square of the Number is divided by 6:
- Let's consider the number x as 6q + 3, where q is the quotient.
- The square of x can be represented as (6q + 3)^2 = 36q^2 + 36q + 9.
- On simplifying, we get (36q^2 + 36q + 9) = 6(6q^2 + 6q) + 3.
- This shows that when the square of a number x is divided by 6, it leaves a remainder of 3.
Therefore, the remainder when the square of a number is divided by 6 is 3, which corresponds to option 'B'.
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