Don't you hate the Long Division Method now?

Algebra Level 2

$\sqrt{1+4 \times 13576 \times 13577}=?$

Challenge: Try to solve this without using a calculator

1 solution

Arkajyoti Banerjee
Jun 12, 2016

We have:

$\sqrt{1+4 \times 13576 \times 13577} = \sqrt{1+4(13576)(13576+1)}$

Now, let $n=13576$ , then the above expression becomes:

$\sqrt{1+4n(n+1)} = \sqrt{4n^{2} + 4n + 1} = \sqrt{(2n+1)^{2}} = 2n+1 = 2 \times 13576 + 1 = \boxed{27153}$

Right on, did the same. Ed Gray

Edwin Gray - 2 years, 8 months ago

Sqrt[ 1+4 * n * (n+1) ] = Sqrt[ 1+2 * 2 * n * (n+1) ] = Sqrt[ 1+2n * (2n+2) ] = Sqrt[ 1+ (2n+1 +1) * (2n+1 - 1) ] = Sqrt[ 1+ (2n+1)^2 - 1] = 2n + 1

Eric Scholz - 2 years, 4 months ago