Verified answer

[tex]a) \: \: \: \: \: \sqrt{2} \times \sqrt{0.(2)} = \sqrt{2 \times 0.(2)} = \sqrt{2 \times \frac{2}{9} } = \sqrt{ \frac{4}{9} } = \frac{2}{3} [/tex]

[tex]b) \: \: \: \: \: \sqrt{0.(2)} \times \sqrt{0.(8)} = \sqrt{0.(2) \times 0.(8)} = \sqrt{ \frac{2}{9} \times \frac{8}{9} } = \sqrt{ \frac{16}{81} } = \frac{4}{9} [/tex]

[tex]c) \: \: \: \: \: \frac{ \sqrt{13} }{ \sqrt{1.(4)} } = \sqrt{ \frac{13}{1.(4)} } = \sqrt{13 \div 1 \frac{4}{9} } = \sqrt{13 \div \frac{13}{9} } = \sqrt{13 \times \frac{9}{13} } = \sqrt{9} = 3[/tex]

[tex]d) \: \: \: \: \: \frac{ \sqrt{1.(7)} }{ \sqrt{0.(4)} } = \sqrt{ \frac{1.(7)}{0.(4)} } = \sqrt{ \frac{1 \frac{7}{9} }{ \frac{4}{9} } } = \sqrt{ \frac{16}{9} \div \frac{4}{9} } = \sqrt{ \frac{16}{9} \times \frac{9}{4} } = \sqrt{4} = 2[/tex]

Ответ:

Пошаговое объяснение:

a)  √2*√0.(2)=√2*√(2/9)=√2*(√2)/3=2/3=0.(6);

b)  √0.(2)*√0.(8)=√2/9*√8/9=√((2*8)/9)=√16/9=4/3=1.(3);

c)  √13/√1.(4) = √13/√(1 4/9)=√13*√(13/9)=(√13*√13)/3=13/3=4.(3);

d)  √1.(7)/√0.(4)=√(1 7/9)√(4/9)=√16/9*√4/9=4/3*2/3=8/9=0.(8).