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What is that least number that must be added to the product 684 × 686 to make it a perfect square?
  • a)
    685
  • b)
    1
  • c)
    684
  • d)
    686
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What is that least number that must be added to the product 684 ×...
684 × 686 = 684 × (684 + 2) = 6842 + 2 × 684
To make it perfect square we should add 1
⇒ 6842 + 2 × 684 × 1 + 12 = (684 + 1)2
So ans is 1.
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Most Upvoted Answer
What is that least number that must be added to the product 684 ×...
Understanding the Problem
To find the least number that must be added to the product of 684 and 686 to make it a perfect square, we first calculate the product.
Calculating the Product
- The product can be expressed as:
- 684 × 686 = 684² - 1 (using the difference of squares)
- Calculating 684²:
- 684² = 466256
- Therefore:
- 684 × 686 = 466256 - 1 = 466255
Finding the Nearest Perfect Square
Next, we need to find the nearest perfect square greater than 466255.
- The square root of 466255 is approximately 683.5.
- The nearest perfect squares are:
- (683)² = 465689
- (684)² = 466256
Determining the Difference
- Since 466256 (which is 684²) is the nearest perfect square greater than 466255, we calculate the difference:
- Difference = 466256 - 466255 = 1
Conclusion
Thus, the least number that must be added to 684 × 686 to make it a perfect square is:
- Answer: 1 (Option B)
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What is that least number that must be added to the product 684 × 686 to make it a perfect square?a)685b)1c)684d)686Correct answer is option 'B'. Can you explain this answer?
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