[tex]a)~~\sqrt{4^4}=\sqrt{(4^2)^2}=4^2=16\\b)~~\sqrt{(-7)^2}=\sqrt{7^2}=7\\c)~~\sqrt{5^4\cdot2^2}=\sqrt{(5^2\cdot2)^2}=5^2\cdot2=50\\d)~~\sqrt{8\cdot162}=\sqrt{2^3\cdot9^2\cdot2}=\sqrt{2^4\cdot9^2}=\sqrt{(2^2\cdot9)^2}=2^2\cdot9=36[/tex]
[tex]e)~~\sqrt{3\cdot21\cdot7}=\sqrt{3\cdot3\cdot7\cdot7}=\sqrt{3^2\cdot7^2}=3\cdot7=21\\f)~~\sqrt{27000\cdot30}=\sqrt{3^3\cdot10^3\cdot3\cdot10}=\sqrt{3^4\cdot10^4}=\sqrt{(3^2\cdot10^2)^2}=3^2\cdot10^2=900\\g)~~\sqrt{22500}=\sqrt{3^2\cdot5^2\cdot10^2}=\sqrt{(3\cdot5\cdot10)^2}=3\cdot5\cdot10=150\\h)~~\sqrt{0,0009}=\sqrt{3^2\cdot0,1^4}=\sqrt{(3\cdot0,1^2)}=3\cdot0,1^2=0,03[/tex]
[tex]i)~~\sqrt{12,25}=\sqrt{7^2\cdot5^2\cdot0,1^2}=\sqrt{(7\cdot5\cdot0,1)^2}=7\cdot5\cdot0,1=3,5\\j)~~\sqrt{4,41}=\sqrt{3^2\cdot7^2\cdot0,1^2}=\sqrt{(3\cdot7\cdot0,1)^2}=3\cdot7\cdot0,1=2,1\\k)~~\sqrt{\frac{12}{75}}=\sqrt{\frac{2^2\cdot3}{5^2\cdot3}}=\sqrt{\frac{2^2}{5^2}}=\sqrt{(\frac25)^2}=\frac25\\l)~~\sqrt{\frac{98}{128}}=\sqrt{\frac{7^2\cdot2}{8^2\cdot2}}=\sqrt{\frac{7^2}{8^2}}=\sqrt{(\frac78)^2}=\frac78[/tex]
[tex]m)~~\sqrt{7\frac{9}{16}}=\sqrt{\frac{121}{16}}=\sqrt{\frac{11^2}{4^2}}=\sqrt{(\frac{11}{4})^2}=\frac{11}{4}=2\frac34\\n)~~\sqrt{4\sqrt{16}}=\sqrt{4\sqrt{4^2}}=\sqrt{4\cdot4}=\sqrt{4^2}=4[/tex]
