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find the square root of √(999x1000x1001x1002+1) can you help me please

find the square root
of √(999x1000x1001x1002+1) can you help me please
 

Grade:11

1 Answers

mycroft holmes
272 Points
6 years ago
We have n(n+1)(n+2)(n+3)+1 = (n2+3n)(n2+3n+2)+1 
 
Let y = n2+3n
 
Then, the given expression is y(y+2)+1 = y2+2y+1 = (y+1)2 = (n2+3n+1)2.
 
Hence, the square root is n2+3n+1 . Substitue n = 999, and you get the square root as 1000999
 
 

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