# Math Help - Another Binomial theorem

1. ## Another Binomial theorem

By assuming $0<\sqrt{5}-2<\frac{1}{4}$ , deduce that the difference between $(\sqrt{5}+2)^5$ and an integer is less than $\frac{1}{1024}$

2. Originally Posted by thereddevils
By assuming $0<\sqrt{5}-2<\frac{1}{4}$ , deduce that the difference between $(\sqrt{5}+2)^5$ and an integer is less than $\frac{1}{1024}$

These are what i can think of :

$0+4<\sqrt{5}-2+4<\frac{1}{4}+4$

$4<\sqrt{5}+2<\frac{5}{4}$

$4^5<(\sqrt{5}+2)^5<(\frac{17}{4})^5$

BUt i still don see the solution to these question .