Question

Показать справедливость неравенства 
1.3,4<$sqrt{12}$<3,6
2. 5<$sqrt{26}$<5,1

Answer 1

1. $3,4< sqrt{12} <3,6$
$3,4=3 frac{4}{10} =frac{34}{10}= frac{17}{5}=sqrt{ frac{289}{25}}$
$sqrt{12} = sqrt{ frac{300}{25} }$
$3,6 = 3 frac{6}{10} = frac{36}{10} = frac{18}{5}= sqrt{frac{324}{25}}$
$sqrt{ frac{289}{25}}<sqrt{ frac{300}{25}}<sqrt{ frac{324}{25} }$
2. $5< sqrt{26} <5,1$
$5= sqrt{25}= sqrt{ frac{2500}{100} }$
$5,1=5 frac{1}{10} = frac{51}{10} = sqrt{ frac{2601}{100} }$
$sqrt{26} = sqrt{ frac{2600}{100}}$
$sqrt{ frac{2500}{100} }< sqrt{ frac{2600}{100}}< sqrt{ frac{2601}{100} }$