The Root of the Problem

Algebra Level 3

For how many different positive integers n n does n \sqrt{n} differ from 100 \sqrt{100} by less than 1?


The answer is 39.

Deva Craig by Deva Craig , 22, USA

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1 solution

Ojasee Duble
Feb 21, 2017

√100 = 10

Now, two nearest perfect squares are 121 (√121 = 11) and 81 (√81 = 9) whose value differs by 1 than the value of √100

Therefore, 121 - 100 = 21 and 100 - 81 = 19

But we don't consider the numbers 121 itself as the difference of their square root = 1

So, according to the given conditions, n = 101 to 120 i.e 20 numbers and 81 to 99 i.e 19 numbers

Thus, 20 + 19 = 39

Ans. n = 39

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I think it should be "82 to 100".

Kushal Patankar - 4 years, 3 months ago

If we will take 81 then 9 and 10 differ by 1

Prakhar Singh - 4 years, 3 months ago

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