Question

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Answer 1

a) $2 \ \textless \ \sqrt{7} \ \textless \ 3$ (ridici totul la patrat)
4 < 7 < 9 - Adevarat 
b) $-4 \ \textless \ -\sqrt{10} \ \textless \ -3$ | x (-1)
$3 \ \textless \ \sqrt{10} \ \textless \ 4$ (ridici la patrat)
9 < 10 < 16 - Adevarat 
c) $\sqrt{0,4} = \sqrt( \frac{4}{10} ) = \frac{ \sqrt{4} }{ \sqrt{10} } = \frac{2}{ \sqrt{10} }$ ∉ Q - Fals 
d) $\sqrt{0,14} = \sqrt{ \frac{14}{100} } = \frac{ \sqrt{14}}{ \sqrt{100}} = \frac{ \sqrt{14}}{10}$ ∉ Q - Fals
e) $\sqrt{2,25} = \sqrt{ \frac{225}{100}} = \frac{ \sqrt{225}}{ \sqrt{100}} = \frac{15}{10} = \frac{3}{2}$ ∉ R\Q - Fals 
f) $\sqrt{1,6} = \frac{ \sqrt{16} }{ \sqrt{10} } = \frac{4}{ \sqrt{10} }$∈R\Q - Adevarat 
g) $\sqrt{0.16} = \frac{ \sqrt{16} }{ \sqrt{100} } = \frac{4}{10} = \frac{2}{5}$∈Q - Adevarat 
h) $\sqrt{0.(16)} = \frac{ \sqrt{16} }{ \sqrt{99} } = \frac{4}{ \sqrt{99} }$∉Q - Fals
i) Rezolvam intain suma 
S = 1+3+ 5+...+11
nr. termeni = (11-1):2+1 = 10:2+1= 5+1 = 6
S= [tex] \frac{(11+1)*6}{2} = \frac{12*6}{2} = 6*6 = 36 [/tex]
$\sqrt{S} = \sqrt{36} = 6$∈Q - Adevarat