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What is the difference between the smallest perfect square larger than 1 million and the largest perfect square smaller than 1 million?
Wiki User
∙ 7y ago
1 million = 1,000,000 = 1000²
Which means we want: (1000 + 1)² - (1000 - 1)² , that is 1001² - 999²
However, before we work that out, lets look at what we have.
let a = 1000, b = 1, then:
(1000 + 1)² - (1000 - 1)² = (a + b)² - (a - b)²
Now (a + b)² = a² +2ab + b²
and (a - b)² = a² - 2ab - b²
→ (a + b)² - (a - b)² = a² +2ab + b² - (a² - 2ab - b²) = 4ab
As a = 1000, b = 1, this means (1000 + 1)² - (1000 -1)² = 4 × 1000 × 1 = 4000.
Wiki User
∙ 7y ago
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