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# Help!

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Find the smallest positive integer n ≥ 100 such that {√n} >1/2.

Note: for a real number x, {x} = x − $$\lfloor x \rfloor$$denotes the fractional part of x.

Jun 16, 2021

### Best Answer

#1
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You can do this by trial and error. Since $$\sqrt{110 } \ is\ approximately\ 10.4880884817$$ with fractiona part equal to

$$10.4880884817 -10 = 0.4880884817<0.5$$,

and $$\sqrt{111}$$ is approximately $$10.5356537529$$with fractional part equal to

$$10.5356537529 -10=0.5356537529>0.5$$,

n = 111 must be the number you are looking for.

Jun 16, 2021

### 1+0 Answers

#1
+1
Best Answer

You can do this by trial and error. Since $$\sqrt{110 } \ is\ approximately\ 10.4880884817$$ with fractiona part equal to

$$10.4880884817 -10 = 0.4880884817<0.5$$,

and $$\sqrt{111}$$ is approximately $$10.5356537529$$with fractional part equal to

$$10.5356537529 -10=0.5356537529>0.5$$,

n = 111 must be the number you are looking for.

Guest Jun 16, 2021