How do you find the closest square number to another number without using a calculator
Say we try to find the closest square number to 26. we already know the closest square number is $25$. However, how do I calculate out 25?
Because, if I try to prime factorize it like so:
$\sqrt{26}$ = $\sqrt{2*13}$And I try to round 13 to the closest even number, I would get this equation here from prime factorization:
$\sqrt{26}$ = $\sqrt{2*13}$
-> $\sqrt{2*2*2*3}$
Then, if I write out the equation, it wouls turn up as:
$\sqrt{24}$ ,
Which is not 25.
I there a way to find out the closest square number to a certain number without using a calculator?
$\endgroup$ 41 Answer
$\begingroup$You have to subtract all the digits but the first one from the number then add this to the original number. e.g with 745, we would subtract the 45 as those are the digits after the first one. We are left with 700, we add 700 to 745 therefore are answer will be 1445. Weeeee did it!!
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