Question

Показать справедливость неравенства 1.3,4< < 3,6 2. 5< < 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. $5< \sqrt{26} <5,1$
$5= \sqrt{25}= \sqrt{ \frac{2500}{100} }$
$5,1=5 \frac{1}{10} = \frac{51}{10} = \sqrt{ \frac{2601}{100} }$
$\sqrt{26} = \sqrt{ \frac{2600}{100}}$
$\sqrt{ \frac{2500}{100} }< \sqrt{ \frac{2600}{100}}< \sqrt{ \frac{2601}{100} }$