a)
\sqrt {6-2\sqrt 5}*\sqrt{6+2\sqrt 5}=\sqrt{(6-2\sqrt5)(6+2\sqrt5)}=\sqrt{36-(2\sqrt5)^2}=
=\sqrt{36-4*5}=\sqrt{16}=4
b)
\sqrt{3\sqrt 7+\sqrt{14}}*\sqrt{3\sqrt7-\sqrt{14}}=\sqrt{(3\sqrt 7+\sqrt{14})(3\sqrt7-\sqrt{14})}=\sqrt{(3\sqrt7)^2-(\sqrt{14})^2}=
=\sqrt{9*7-14}=\sqrt{49}=7
c)
\sqrt{4\sqrt 5-2\sqrt{11}}*\sqrt{4\sqrt5+2\sqrt{11}}=\sqrt{(4\sqrt5-2\sqrt{11})(4\sqrt5+2\sqrt{11})}=\sqrt{(4\sqrt5)^2-(2\sqrt{11})^2}=
\sqrt{16*5-4*11}=\sqrt{80-44}=\sqrt{36}=6
Zastosowano wzór skróconego mnożenia:
a^2-b^2=(a+b)(a-b) różnica kwadratów