<s>[INST] $a, b$ are the integer part and decimal fraction of $\sqrt7$ find integer part of $\frac{a}{b}$ 
$a, b$ are the integer part and decimal fraction of $\sqrt7$
find integer part of $\frac{a}{b}$

using calculator :
$\sqrt 7$ = 2.645
$\frac{a}{b} = \frac{2}{0.6} = \frac{20}{6} = 3.333$
integer part of $\frac{a}{b} = 3$
how to do it without calculator? if i don't know $\sqrt7$ part
 [/INST] Note that $$ 2.5<\sqrt 7<3$$
$$ \frac {a}{b} = \frac {2}{\sqrt 7 -2} = \frac {2(\sqrt 7+2)}{3}$$
$$3= \frac {2( 2.5+2)}{3} <        \frac {2(\sqrt 7+2)}{3} <\frac {2( 3+2)}{3}<4$$
Thus the integer part of $\frac {2}{\sqrt 7 -2}$ is $3$
</s>