[tex]\displaystyle \mathtt{2a)M_g= \sqrt{12 \cdot 3}= \sqrt{36}=6 }\\ \\ \mathtt{b) M_g=\sqrt{8 \cdot 2}= \sqrt{16}=4 }\\ \\ \mathtt{c) M_g=\sqrt{18 \cdot 8}= \sqrt{144}=12 }\\ \\ \mathtt{d) M_g=\sqrt{3 \frac{1}{5} \cdot5}= \sqrt{ \frac{16}{5}\cdot 5 }= \sqrt{16}=4}\\ \\ \mathtt{e) M_g=\sqrt{ \frac{7}{12} \cdot 2 \frac{1}{3}}= \sqrt{ \frac{7}{12} \cdot \frac{7}{3} }= \sqrt{ \frac{49}{36} }= \frac{ \sqrt{49} }{ \sqrt{36} } = \frac{7}{6} }[/tex]
[tex]\displaystyle \mathtt{f)M_g= \sqrt{\sqrt{5}^{-1} \cdot \sqrt{ \frac{5}{16} } }= \sqrt{ \frac{1}{ \sqrt{5} }\cdot \frac{ \sqrt{5} }{ \sqrt{16} } }= \sqrt{ \frac{1}{4} }= \frac{ \sqrt{1} }{ \sqrt{4} }= \frac{1}{2} }[/tex]
[tex]\displaystyle \mathtt{3a)M_g= \sqrt{\left(5 \sqrt{2} +7 \right)\left(5 \sqrt{2}-7\right) }= \sqrt{50-49} = \sqrt{1}=1 }\\ \\ \mathtt{b)M_g= \sqrt{2 \sqrt{24} \cdot 9 \sqrt{6}}= \sqrt{2 \cdot 2 \sqrt{6}\cdot 9 \sqrt{6} }=\sqrt{4 \sqrt{6}\cdot 9 \sqrt{6}} = \sqrt{216}=6 \sqrt{6}}\\ \\ \mathtt{c)M_g= \sqrt{0,09 \cdot 100}= \sqrt{ \frac{9}{100} \cdot 100} = \sqrt{9}=3 }\\ \\ \mathtt{d) M_g=\sqrt{\left(4-2 \sqrt{3} \right)\left(4+2 \sqrt{3} \right)}= \sqrt{16-12}= \sqrt{4}=2}[/tex]
[tex]\displaystyle \mathtt{e)M_g= \sqrt{ \sqrt{2}\cdot \sqrt{8} }= \sqrt{ \sqrt{2}\cdot 2 \sqrt{2} }= \sqrt{4} = 2} \\ \\ \mathtt{f)M_g= \sqrt{\left(3 \sqrt{5}-6\right)\left(3 \sqrt{5}+6\right)}= \sqrt{45-36}= \sqrt{9}=3 }[/tex]
[tex]\displaystyle \mathtt{4)a=5 \sqrt{12}+3 \sqrt{27}-9 \sqrt{3} }\\ \\ \mathtt{a=5 \cdot 2 \sqrt{3}+3 \cdot 3 \sqrt{3}-9 \sqrt{3}}\\ \\ \mathtt{a=10 \sqrt{3}+9 \sqrt{3} -9 \sqrt{3}}\\ \\ \mathtt{a=10 \sqrt{3} }\\ \\ \mathtt{b= \sqrt{48}+2 \sqrt{3}- \sqrt{75}}\\ \\ \mathtt{b=4 \sqrt{3}+2 \sqrt{3}-5 \sqrt{3}}\\ \\ \mathtt{b= \sqrt{3} }\\ \\ \mathtt{M_g= \sqrt{10 \sqrt{3}\cdot \sqrt{3}}= \sqrt{30}}[/tex]
[tex]\displaystyle \mathtt{5)x= \sqrt{2}-1 }\\ \\ \mathtt{y=\left| \frac{1}{3 \sqrt{2}}+ \frac{ \sqrt{3}+1 }{6}- \frac{1}{2 \sqrt{3} } \right| \cdot 6}\\ \\ \mathtt{y=\left| \frac{ \sqrt{2} }{6}+ \frac{ \sqrt{3}+1 }{6}- \frac{ \sqrt{3} }{6}\right| \cdot 6}\\ \\ \mathtt{y=\left| \frac{ \sqrt{2}+ \sqrt{3}+1- \sqrt{3}}{6}\right| \cdot 6 }\\ \\ \mathtt{y=\left| \frac{ \sqrt{2}+1 }{6}\right| \cdot 6 }\\ \\ \mathtt{y= \frac{ \sqrt{2} +1}{6}\cdot 6 }\\ \\ \mathtt{y= \sqrt{2}+1 }[/tex]
[tex]\displaystyle \mathtt{M_g= \sqrt{\left( \sqrt{2}-1\right)\left( \sqrt{2}+1\right) }= \sqrt{2-1}= \sqrt{1}=1 } [/tex]
[tex]\displaystyle \mathtt{6)a=3 \frac{1}{5}\cdot \left[1,(3)+3 \frac{2}{3}\right] \cdot \sqrt{2}}\\ \\ \mathtt{a= \frac{16}{5}\cdot \left( \frac{4}{3}+ \frac{11}{3}\right) \cdot \sqrt{2} }\\ \\ \mathtt{a= \frac{16}{5}\cdot \frac{15}{3} \cdot \sqrt{2}}\\ \\ \mathtt{a= \frac{16}{5}\cdot 5 \cdot \sqrt{2}}\\ \\ \mathtt{a=16 \sqrt{2} }[/tex]
[tex]\displaystyle \mathtt{b=\left( \frac{ \sqrt{50} }{2} + \frac{ \sqrt{18} }{3}- \frac{ \sqrt{2} }{2}+ \frac{45}{5 \sqrt{2} }\right):4 }\\ \\ \mathtt{b=\left( \frac{5 \sqrt{2} }{2}+ \frac{3 \sqrt{2} }{3}- \frac{ \sqrt{2} }{2}+ \frac{45 \sqrt{2} }{10}\right):4 }\\ \\ \mathtt{b=\left( \frac{5 \sqrt{2} }{2}+ \sqrt{2}- \frac{ \sqrt{2} }{2}+ \frac{45 \sqrt{2} }{10}\right):4}\\ \\ \mathtt{b= \frac{25 \sqrt{2}+10 \sqrt{2}-5 \sqrt{2}+45 \sqrt{2} }{10}:4 }[/tex]
[tex]\displaystyle \mathtt{b= \frac{75 \sqrt{2} }{10}\cdot \frac{1}{4}} \\ \\ \mathtt{b= \frac{75 \sqrt{2} }{40} }\\ \\ \mathtt{b= \frac{15 \sqrt{2} }{8} }\\ \\ \mathtt{M_g= \sqrt{16 \sqrt{2}\cdot \frac{15 \sqrt{2} }{8}}=\sqrt{2 \sqrt{2}\cdot 15 \sqrt{2} }= \sqrt{60}=2 \sqrt{15} }[/tex]
