1)

[tex]\displaystyle \sqrt{32}=\sqrt{16*2}=4\sqrt{2}\\\\\sqrt{0.27}=\sqrt{\frac{27}{100}}=\frac{1}{10}*\sqrt{9*3}=0.3\sqrt{3}\\\\\sqrt{\frac{5}{49}}=\frac{1}{7}\sqrt{5}\\\\\sqrt{x^3}=|x|\sqrt{x}\\\\\sqrt{28a^7}=\sqrt{4*7a^6*a}=25|a^3|\sqrt{7a}\\\\\sqrt{-75a^5}=\sqrt{-25*3*a^4*a}=5a^2\sqrt{-3a}[/tex]

2)

[tex]\displaystyle 0.1\sqrt{3*100}+\frac{1}{3}*\sqrt{3*9}-\frac{5}{7}*\sqrt{49*3}=\sqrt{3}+\sqrt{3}-5\sqrt{3}=-3\sqrt{3}[/tex]