Răspuns:
Explicație pas cu pas:
a)
[tex]\sqrt{2^3} = \sqrt{2^2\cdot 2} = 2\sqrt{2}[/tex]
b)
[tex]\sqrt{2^5} = \sqrt{2^4\cdot 2} = 2^2\sqrt{2} = 4\sqrt{2}[/tex]
c)
[tex]\sqrt{3^7} = \sqrt{3^6\cdot 3} = 3^3\sqrt{3} = 27\sqrt{3}[/tex]
d)
[tex]2\sqrt{2^{11}} = 2\sqrt{2^{10}\cdot 2} = 2\cdot2^5\sqrt{2} = 2^6\sqrt{2} = 64\sqrt{2}[/tex]
e)
[tex]-6\sqrt{2^3} =-6 \sqrt{2^2\cdot 2} = -6\cdot 2\sqrt{2} = -12\sqrt{2}[/tex]
f)
[tex]\sqrt{2^3\cdot3^2} = \sqrt{2^2\cdot 2\cdot3^2} = 2\cdot3\sqrt{2} = 6\sqrt{2}[/tex]
g)
[tex]-\sqrt{3^4\cdot5^7} = -\sqrt{3^4\cdot 5^6\cdot5} =- 3^2\cdot5^3\cdot\sqrt{5} =-9\cdot125 \sqrt{5}=-1125\sqrt{5}[/tex]
h)
[tex]\sqrt{2^5\cdot3^4 \cdot5^7} = \sqrt{2^4\cdot 2\cdot3^4\cdot5^6\cdot5} = 2^2\cdot3^2\cdot5^3\cdot\sqrt{2\cdot5} = 4\cdot9\cdot125\sqrt{10} = 4500\sqrt{10}[/tex]
i)
[tex]\sqrt{3^6\cdot5^5 \cdot11^2} = \sqrt{3^6\cdot 5^4\cdot5\cdot11^2} = 3^3\cdot5^2\cdot11\sqrt{5} = 27\cdot25\cdot11\sqrt{5} = 7425\sqrt{5}[/tex]
j)
[tex]\sqrt{2^{2n+1}\cdot3^{4n} } = \sqrt{2^{2n}\cdot 2\cdot3^{4n}} = 2^n\cdot3^{2n}\cdot\sqrt{2}[/tex]
