[tex]\it a)\ \sqrt{5^3\cdot5}=\sqrt{5^4}=\sqrt{(5^2)^2}=5^2=25\\ \\ b)\ \sqrt{7^4\cdot4}=\sqrt{(7^2)^2\cdot4}=\sqrt{49^2\cdot4}=49\cdot2=98\\ \\ c)\ \sqrt{3^4\cdot5^2\cdot36}=\sqrt{81\cdot25\cdot36}=9\cdot5\cdot6=9\cdot30=270\\ \\ d)\ \sqrt{144\cdot3^2\cdot64}=12\cdot3\cdot8=288\\ \\ \ell)\ \sqrt{5(9^2-6^2)}=\sqrt{5\cdot45}=\sqrt{5\cdot5\cdot9}=\sqrt{25\cdot9}=5\cdot3=15\\ \\ f)\ \sqrt{9^2-6^2+2^2}=\sqrt{81-36+4}=\sqrt{49}=7\\ \\ e)\sqrt{21^2\cdot23^2}=21\cdot23[/tex]
