13.
a) [tex]5\sqrt{3} = \sqrt{5^2} \cdot \sqrt{3} = \sqrt{25} \cdot \sqrt{3} = \sqrt{75}[/tex]
b) [tex]7\sqrt{2} =\sqrt{49 \cdot 2} = \sqrt{98}[/tex]
c) [tex]6\sqrt{\frac{5}{6} } = \sqrt{36 \cdot \frac{5}{6} } = \sqrt{6 \cdot 5} = \sqrt{30}[/tex]
d) [tex]\frac{1}{2} \sqrt{12} = \sqrt{\left( \frac{1}{2} \right) ^2 \cdot 12} = \sqrt{\frac{1}{4} \cdot 12 } = \sqrt{3}[/tex]
e) [tex]0,1\sqrt{2000}=\sqrt{\left( 0,1 \right)^2 \cdot 2000} = \sqrt{0,01 \cdot 2000} = \sqrt{20}[/tex]
f) [tex]4\sqrt[3]{\frac{3}{32} } = \sqrt[3]{4^3 \cdot \frac{3}{32} } = \sqrt[3]{64 \cdot \frac{3}{32} } = \sqrt{2 \cdot 3} = \sqrt{6}[/tex]
g) [tex]0,2\sqrt[3]{50} = \sqrt[3]{0,008 \cdot 50} = \sqrt[3]{0,4}[/tex]
h) [tex]0,3\sqrt{40} = \sqrt{0,09 \cdot 40}=\sqrt{3,6}[/tex]
14.
a)
[tex]3\sqrt{3} = \sqrt{9 \cdot 3} = \sqrt{27}[/tex]
[tex]2\sqrt{6} = \sqrt{4 \cdot 6} = \sqrt{24}[/tex]
[tex]4\sqrt{2} = \sqrt{16 \cdot 2} = \sqrt{32}[/tex]
[tex]\sqrt{24} < \sqrt{27} < \sqrt{29} < \sqrt{32}[/tex]
[tex]2\sqrt{6} < 3\sqrt{3} < \sqrt{29} < 4\sqrt{2}[/tex]
b)
[tex]2\sqrt[3]{5} = \sqrt[3]{8 \cdot 5}=\sqrt[3]{40}[/tex]
[tex]5\sqrt[3]{2} = \sqrt[3]{125 \cdot 2} = \sqrt[3]{250}[/tex]
[tex]4\sqrt[3]{3} = \sqrt[3]{64 \cdot 3} = \sqrt[3]{192}[/tex]
[tex]\sqrt[3]{40} < \sqrt[3]{123} < \sqrt[3]{192} < \sqrt[3]{250}[/tex]
[tex]2\sqrt[3]{5} < \sqrt[3]{123} < 4\sqrt[3]{3} < 5\sqrt[3]{2}[/tex]
