Răspuns:
Explicație pas cu pas:
a)
[tex]\sqrt{2^7} = \sqrt{2^{6+1}} =\sqrt{2^6*2} = \sqrt{2^6} *\sqrt{2} =2^3*\sqrt{2}[/tex]
b)
[tex]\sqrt{3^{11}} = \sqrt{3^{10+1}} =\sqrt{3^{10}*3} = \sqrt{3^{10}} *\sqrt{3} =3^5*\sqrt{3}[/tex]
c)
[tex]\sqrt{2^5*3^7} = \sqrt{2^{4+1}*3^{6+1}} =\sqrt{2^4*2*3^6*3} = \sqrt{2^4}*\sqrt{3^6} *\sqrt{2*3} =2^2*3^3*\sqrt{6}[/tex]
d)
[tex]\sqrt{3^3*5^5*7^7} = \sqrt{3^{2+1}*5^{4+1}*7^{6+1}} =\sqrt{3^2*3*5^4*5*7^6*7} = \sqrt{3^2}*\sqrt{5^4}*\sqrt{7^6} *\sqrt{3*5*7} =3*5^2*7^3*\sqrt{105}[/tex]
e)
[tex]\sqrt{(-2)^3*(-3)^3} =\sqrt{[(-2)*(-3)]^3}=\sqrt{6^3} = \sqrt{6^{2+1}} =\sqrt{6^2}*\sqrt{6}=6*\sqrt{6}= 2*3*\sqrt{6}[/tex]
f)
[tex]\sqrt{2*2^3*2^5*2^8} = \sqrt{2^{1+3+5+8}} = \sqrt{2^{17}} = \sqrt{2^{16+1}} = \sqrt{2^{16}}*\sqrt{2} = 2^8*\sqrt{2}[/tex]
g)
[tex]\sqrt{2^{2n+1}} = \sqrt{2^{2n}}*\sqrt{2} = 2^n*\sqrt{2}[/tex]
h)
[tex]\sqrt{3^{2n+3}} =\sqrt{3^{2n+2+1}}= \sqrt{3^{2n+2}}*\sqrt{3}= \sqrt{3^{2(n+1)}}*\sqrt{3} = 3^{n+1}*\sqrt{3}[/tex]
