Aplicăm:

• dacă \({a, b, x, y \in ℝ}\) și \({x, y \ge 0}\), atunci:



\({a\sqrt{x} \cdot b\sqrt{x} = ab\sqrt{x^2}=abx}\)

\({a\sqrt{x} \cdot b\sqrt{y} = ab\sqrt{xy}}\)

a) \({\sqrt{3} \cdot \sqrt{5} = \sqrt{3 \cdot 5}}\)

a) \({\textcolor{white}{\sqrt{3} \cdot \sqrt{5}} = \sqrt{15}}\)

b) \({\sqrt{2} \cdot \sqrt{10} = \sqrt{2 \cdot 10}}\)

b) \({\textcolor{white}{\sqrt{2} \cdot \sqrt{10} }= \sqrt{2 \cdot 2 \cdot 5}}\)

b) \({\textcolor{white}{\sqrt{2} \cdot \sqrt{10} }= \sqrt{2^2 \cdot 5}}\)

b) \({\textcolor{white}{\sqrt{2} \cdot \sqrt{10} }= 2\sqrt{5}}\)

c) \({\sqrt{7} \cdot (-\sqrt{2}) = 1 \cdot \sqrt{7} \cdot (-1)\cdot \sqrt{2}}\)

c) \({\textcolor{white}{\sqrt{7} \cdot (-\sqrt{2})} = [1 \cdot (-1)]\sqrt{7 \cdot 2}}\)

c) \({\textcolor{white}{\sqrt{7} \cdot (-\sqrt{2}) }= (-1)\sqrt{14}}\)

c) \({\textcolor{white}{\sqrt{7} \cdot (-\sqrt{2}) }= -\sqrt{14}}\)

d) \({(-\sqrt{20}) \cdot \sqrt{5} = (-1) \cdot \sqrt{20} \cdot 1 \cdot \sqrt{5}}\)

d) \({\textcolor{white}{(-\sqrt{20}) \cdot \sqrt{5}} = [(-1) \cdot 1] \cdot \sqrt{20 \cdot 5}}\)

d) \({\textcolor{white}{(-\sqrt{20}) \cdot \sqrt{5}} = (-1) \cdot\sqrt{100}}\)

d) \({\textcolor{white}{(-\sqrt{20}) \cdot \sqrt{5}} = (-1) \cdot \sqrt{10^2}}\)

d) \({\textcolor{white}{(-\sqrt{20}) \cdot \sqrt{5}} = (-1) \cdot 10}\)

d) \({\textcolor{white}{(-\sqrt{20}) \cdot \sqrt{5}} = -10}\)

e) \({3\sqrt{7} \cdot (-\sqrt{7}) =3\sqrt{7} \cdot (-1) \cdot \sqrt{7}}\)

e) \({\textcolor{white}{3\sqrt{7} \cdot (-\sqrt{7})} = [3 \cdot (-1) ] \cdot \sqrt{7 \cdot 7} }\)

e) \({\textcolor{white}{3\sqrt{7} \cdot (-\sqrt{7})} = (-3) \cdot \sqrt{7 ^2} }\)

e) \({\textcolor{white}{3\sqrt{7} \cdot (-\sqrt{7})} = (-3) \cdot 7 }\)

e) \({\textcolor{white}{3\sqrt{7} \cdot (-\sqrt{7})} = -21 }\)

f) \({(-2\sqrt{6}) \cdot (-3\sqrt{10}) = [(-2) \cdot (-3)] \cdot \sqrt{6 \cdot 10}}\)

f) \({\textcolor{white}{(-2\sqrt{6}) \cdot (-3\sqrt{10})} = 6 \cdot \sqrt{2 \cdot 3 \cdot 2 \cdot5}}\)

f) \({\textcolor{white}{(-2\sqrt{6}) \cdot (-3\sqrt{10})} = 6 \cdot \sqrt{2^2 \cdot 3 \cdot 5}}\)

f) \({\textcolor{white}{(-2\sqrt{6}) \cdot (-3\sqrt{10})} = 6 \cdot 2 \sqrt{15}}\)

f) \({\textcolor{white}{(-2\sqrt{6}) \cdot (-3\sqrt{10})} = 12 \sqrt{15}}\)

g) \({(-6\sqrt{5}) \cdot (-4\sqrt{11}) = [(-6) \cdot (-4)] \cdot \sqrt{5 \cdot 11}}\)

g) \({\textcolor{white}{(-6\sqrt{5}) \cdot (-4\sqrt{11}) }= 24 \cdot \sqrt{55}}\)

g) \({\textcolor{white}{(-6\sqrt{5}) \cdot (-4\sqrt{11}) }= 24 \sqrt{55}}\)

a) \({2\sqrt{6} \cdot 5\sqrt{3} = (2\cdot 5) \cdot \sqrt{6 \cdot 3}}\)

a) \({\textcolor{white}{2\sqrt{6} \cdot 5\sqrt{3}} = 10 \cdot \sqrt{2 \cdot 3 \cdot 3}}\)

a) \({\textcolor{white}{2\sqrt{6} \cdot 5\sqrt{3} }= 10 \cdot \sqrt{2 \cdot 3^2}}\)

a) \({\textcolor{white}{2\sqrt{6} \cdot 5\sqrt{3}} = 10 \cdot 3 \cdot \sqrt{2 }}\)

a) \({\textcolor{white}{2\sqrt{6} \cdot 5\sqrt{3} }= 30\sqrt{2 }}\)

b) \({-\sqrt{5} \cdot 4\sqrt{18} = (-1) \cdot \sqrt{5} \cdot 4\sqrt{3^2 \cdot 2}}\)

b) \({\textcolor{white}{-\sqrt{5} \cdot 4\sqrt{18}} = [(-1) \cdot 4] \cdot \sqrt{5 \cdot 3^2 \cdot 2}}\)

b) \({\textcolor{white}{-\sqrt{5} \cdot 4\sqrt{18}} = (-4) \cdot 3 \cdot \sqrt{5 \cdot 2}}\)

b) \({\textcolor{white}{-\sqrt{5} \cdot 4\sqrt{18}} = -12 \sqrt{10}}\)

c) \({(-7\sqrt{14}) \cdot (-3\sqrt{11}) =[(-7) \cdot (-3) ] \cdot \sqrt{14 \cdot 11}}\)

c) \({\textcolor{white}{(-7\sqrt{14}) \cdot (-3\sqrt{11})} =21\sqrt{154}}\)

d) \({10 \cdot (-3\sqrt{2}) = [10 \cdot (-3)] \cdot \sqrt{2}}\)

d) \({\textcolor{white}{10 \cdot (-3\sqrt{2})} = -30\sqrt{2}}\)

e) \({8\sqrt{8} \cdot (-6\sqrt{6}) =8 \cdot (-6) \cdot \sqrt{8 \cdot 6}}\)

e) \({\textcolor{white}{8\sqrt{8} \cdot (-6\sqrt{6})} =(-48) \cdot \sqrt{2^3 \cdot 2 \cdot 3 }}\)

e) \({\textcolor{white}{8\sqrt{8} \cdot (-6\sqrt{6})} =(-48) \sqrt{2^4 \cdot 3 }}\)

e) \({\textcolor{white}{8\sqrt{8} \cdot (-6\sqrt{6})} =(-48) \sqrt{(2^2)^2 \cdot 3 }}\)

e) \({\textcolor{white}{8\sqrt{8} \cdot (-6\sqrt{6})} =(-48) \sqrt{4^2 \cdot 3 }}\)

e) \({\textcolor{white}{8\sqrt{8} \cdot (-6\sqrt{6})} =(-48) \cdot 4 \cdot \sqrt{ 3 }}\)

e) \({\textcolor{white}{8\sqrt{8} \cdot (-6\sqrt{6})} =-192 \sqrt{ 3 }}\)

f) \({(-9\sqrt{5}) \cdot (-6\sqrt{15}) = (-9) \cdot (-6) \cdot \sqrt{5 \cdot 15}}\)

f) \({\textcolor{white}{(-9\sqrt{5}) \cdot (-6\sqrt{15})} = 54 \sqrt{5 \cdot 5 \cdot 3 }}\)

f) \({\textcolor{white}{(-9\sqrt{5}) \cdot (-6\sqrt{15})} = 54 \sqrt{5^2 \cdot 3 }}\)

f) \({\textcolor{white}{(-9\sqrt{5}) \cdot (-6\sqrt{15})} = 54 \cdot 5 \cdot \sqrt{3 }}\)

f) \({\textcolor{white}{(-9\sqrt{5}) \cdot (-6\sqrt{15})} = 270 \sqrt{3 }}\)

g) \({\sqrt{12} \cdot (-7\sqrt{12}) = 1 \cdot (-7) \cdot \sqrt{12 \cdot 12}}\)

g) \({\textcolor{white}{\sqrt{12} \cdot (-7\sqrt{12}) }= (-7) \cdot \sqrt{12^2}}\)

g) \({\textcolor{white}{\sqrt{12} \cdot (-7\sqrt{12}) }= (-7) \cdot 12}\)

g) \({\textcolor{white}{\sqrt{12} \cdot (-7\sqrt{12}) }= -84}\)

h) \({2\sqrt{2} \cdot 3\sqrt{5} \cdot 6\sqrt{7} = 2 \cdot 3 \cdot 6 \cdot \sqrt{2 \cdot 5 \cdot 7} }\)

h) \({\textcolor{white}{2\sqrt{2} \cdot 3\sqrt{5} \cdot 6\sqrt{7} }= 36 \cdot \sqrt{70} }\)

h) \({\textcolor{white}{2\sqrt{2} \cdot 3\sqrt{5} \cdot 6\sqrt{7} }= 36 \sqrt{70} }\)

i) \({(-\sqrt{3}) \cdot (-2\sqrt{6}) \cdot (-5\sqrt{24}) = (-1) \cdot (-2) \cdot (-5) \cdot \sqrt{3 \cdot 6 \cdot 24} }\)

i) \({\textcolor{white}{(-\sqrt{3}) \cdot (-2\sqrt{6}) \cdot (-5\sqrt{24}) }= (-10) \cdot \sqrt{3 \cdot 3 \cdot 2 \cdot 3 \cdot 2^3} }\)

i) \({\textcolor{white}{(-\sqrt{3}) \cdot (-2\sqrt{6}) \cdot (-5\sqrt{24}) }= (-10) \cdot \sqrt{3^2 \cdot 2^4 \cdot 3} }\)

i) \({\textcolor{white}{(-\sqrt{3}) \cdot (-2\sqrt{6}) \cdot (-5\sqrt{24}) }= (-10) \cdot 3 \cdot 2^2 \cdot \sqrt{3} }\)

i) \({\textcolor{white}{(-\sqrt{3}) \cdot (-2\sqrt{6}) \cdot (-5\sqrt{24}) }= -120\sqrt{3} }\)

j) \({5\sqrt{7} \cdot (-7\sqrt{3}) \cdot (-3\sqrt{2}) = 5 \cdot (-7) \cdot (-3) \cdot \sqrt{7 \cdot 3 \cdot 2}}\)

j) \({\textcolor{white}{5\sqrt{7} \cdot (-7\sqrt{3}) \cdot (-3\sqrt{2})} = 105 \sqrt{42}}\)

k) \({(-6\sqrt{51}) \cdot (-2\sqrt{3}) \cdot (-4\sqrt{17}) = (-6) \cdot (-2) \cdot (-4) \cdot \sqrt{51 \cdot 3 \cdot 17}}\)

k) \({\textcolor{white}{(-6\sqrt{51}) \cdot (-2\sqrt{3}) \cdot (-4\sqrt{17})} = (-48) \cdot \sqrt{51 \cdot 51}}\)

k) \({\textcolor{white}{(-6\sqrt{51}) \cdot (-2\sqrt{3}) \cdot (-4\sqrt{17}) }= (-48) \cdot 51}\)

k) \({\textcolor{white}{(-6\sqrt{51}) \cdot (-2\sqrt{3}) \cdot (-4\sqrt{17})} = -2448}\)