Consecutives Under Root

Algebra Level 1

Compute ( 31 ) ( 30 ) ( 29 ) ( 28 ) + 1 \sqrt{(31)(30)(29)(28)+1}


The answer is 869.

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1 solution

Danish Ahmed
Mar 8, 2015

28 29 30 31 + 1 \sqrt{28\cdot 29\cdot 30\cdot 31 +1}

= ( 28 31 ) ( 29 30 ) + 1 =\sqrt{(28\cdot 31)(29\cdot 30) +1}

= 868 870 + 1 =\sqrt{868\cdot 870 +1}

= ( 869 1 ) ( 869 + 1 ) + 1 =\sqrt{(869-1)(869+1)+1}

= 86 9 2 1 + 1 =\sqrt{869^2-1+1}

= 869 =\boxed{869}

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