An algebra problem by Natan Mendes

Algebra Level 1

3000 × 3000 + 12004 2 = ? \sqrt [ 2 ]{ 3000\times 3000+12004 } =\quad ?


The answer is 3002.

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1 solution

Isaac Buckley
Jul 8, 2015

Notice how 3000 × 3000 + 12004 = 300 0 2 + 12000 + 4 \sqrt{3000\times3000+12004}=\sqrt{3000^2+12000+4} Which is of the form n 2 + 4 n + 4 = ( n + 2 ) 2 = n + 2 \sqrt{n^2+4n+4}=\sqrt{(n+2)^2}=n+2 where n = 3000 n=3000

3000 + 2 = 3002 3000+2=\boxed{3002}

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