Question

For how many positive integers $N$ does $\sqrt{N}$ differ from 10 by less than 2?

Answer 1

given: mod($\sqrt{n}$ - 10) < 2

to find: positive integers between these.

1. mod($\sqrt{n}$ - 10) < 2,    

since question says positive integers,so mod have to be applied.

2. after removing mod -2 has to be written on left side of equation by giving appropriate sign

• -2 < $\sqrt{n}$ - 10 < 2

3. solving the equation further, we get

• 8 < $\sqrt{n}$ < 12

4. squaring both sides,

64 < n < 144