2
$\begingroup$

I recently found a new math riddle that I couldn't solve, it ask you compute the following without a calculator:

$$\sqrt{1+2015\sqrt{1 + 2018 \cdot 2016}}$$

I tried to rewrite both of 2016 as powers of two but I couldn't get anywhere close .

How wouLd you solve this problem ?

$\endgroup$
  • 1
    $\begingroup$ Haha, gues which year it still is? $\endgroup$ – Simply Beautiful Art Dec 10 '16 at 19:52
12
$\begingroup$

$2016\times 2018 = (2017-1)(2017+1) = 2017^2-1$

  • can you take it from there?
$\endgroup$
1
$\begingroup$

In this kind of questions, start by doing what you shouldn't and understand what happens. Using a calculator you see that the final result is $2016$.

Another common thing, is to use standard arithmetic tricks, which seem subtle as the numbers are huge! As Joffan pointed out $2016\times 2018 = (2017-1)\times(2017+1) = 2017^2-1$ you could have seen that by noticing how close the two numbers were, and therefore the standard algebraic formula.

Then you get $2015 \times 2017 = (2016-1)(2016+1) = 2016^2 - 1$ and therefore you get 2016 as the final answer.

You could have seen that from the beginning as you see that $1$s are involved in both squares. You knew the result was $2016$ so you know that $2015\sqrt{1+2018\times 2016}$ must have been $2016^2 - 1$ and from this you could have worked backwards.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.