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Sorry, you've used all 3 tries. You tried 3, 54 and 44.
Solution
Evaluate .29 × 30 × 31 × 32 + 1
− − − − − − − − − − − − − − − − −
√
We will show something more general, namely that .
This is true because
Applying , we get 929 as the numerical answer.
Note: Of course, you can also multiply all the numbers and take the square root of the product.
= | + 3n + 1|n(n + 1)(n + 2)(n + 3) + 1
− − − − − − − − − − − − − − − − − − − − −
√ n2
n(n + 1)(n + 2)(n + 3) + 1 = ( + 3n)( + 3n + 2) + 1n2
n2
= ( + 3n + 1 − 1)( + 3n + 1 + 1) + 1n2
n2
= ( + 3n + 1 − + 1n2
)2
12
= ( + 3n + 1 .n2
)2
n = 29
Computing a Square Root Product
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6/15/2013https://brilliant.org/assessment/kt/solvable_component/indices-and-surds/2245227/