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A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A number when divided by 6 leaves remainder 3. When the square of the ...
Let the number be ‘x’
x = 6y + 3
x2 = (6y + 3)2
x2 = 36y2 + 36y + 9
x2 = 6 × (6y2 + 6y + 1) + 3
∴ When the square of the same number is divided by 6, the remainder will be 3.
x = 6y + 3
x2 = (6y + 3)2
x2 = 36y2 + 36y + 9
x2 = 6 × (6y2 + 6y + 1) + 3
∴ When the square of the same number is divided by 6, the remainder will be 3.
Most Upvoted Answer
A number when divided by 6 leaves remainder 3. When the square of the ...
To solve this problem, we need to use the concept of remainders when dividing by a number. Let's break down the problem step by step:
Step 1: Given that a number, when divided by 6, leaves a remainder of 3. We can represent this as:
Number = 6n + 3, where n is an integer.
Step 2: We need to find the remainder when the square of the number is divided by 6. Let's square the expression we obtained in Step 1:
Number^2 = (6n + 3)^2
= 36n^2 + 36n + 9
Step 3: Now, let's divide the squared number by 6 and find the remainder. We can express this as:
Number^2 = 6m + remainder, where m is an integer.
So, substituting the expression from Step 2:
36n^2 + 36n + 9 = 6m + remainder
Step 4: To find the remainder, we can simplify the equation:
36n^2 + 36n + 9 = 6m + remainder
(6n + 3)(6n + 3) = 6m + remainder
(6n + 3)^2 = 6m + remainder
Step 5: From Step 1, we know that (6n + 3) is the number. So, we can substitute it in Step 4:
(6n + 3)^2 = 6m + remainder
Number^2 = 6m + remainder
Step 6: From Step 5, we can conclude that the remainder when the square of the number is divided by 6 is the same as the remainder when the number itself is divided by 6. Therefore, the remainder is 3 (option D).
In summary, when a number is divided by 6 and leaves a remainder of 3, the remainder when the square of the number is divided by 6 will also be 3.
Step 1: Given that a number, when divided by 6, leaves a remainder of 3. We can represent this as:
Number = 6n + 3, where n is an integer.
Step 2: We need to find the remainder when the square of the number is divided by 6. Let's square the expression we obtained in Step 1:
Number^2 = (6n + 3)^2
= 36n^2 + 36n + 9
Step 3: Now, let's divide the squared number by 6 and find the remainder. We can express this as:
Number^2 = 6m + remainder, where m is an integer.
So, substituting the expression from Step 2:
36n^2 + 36n + 9 = 6m + remainder
Step 4: To find the remainder, we can simplify the equation:
36n^2 + 36n + 9 = 6m + remainder
(6n + 3)(6n + 3) = 6m + remainder
(6n + 3)^2 = 6m + remainder
Step 5: From Step 1, we know that (6n + 3) is the number. So, we can substitute it in Step 4:
(6n + 3)^2 = 6m + remainder
Number^2 = 6m + remainder
Step 6: From Step 5, we can conclude that the remainder when the square of the number is divided by 6 is the same as the remainder when the number itself is divided by 6. Therefore, the remainder is 3 (option D).
In summary, when a number is divided by 6 and leaves a remainder of 3, the remainder when the square of the number is divided by 6 will also be 3.
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A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder isa)0b)1c)2d)3Correct answer is option 'D'. Can you explain this answer?
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