Răspuns:
Explicație pas cu pas:
a)
[tex]\sqrt{2} + \sqrt{8} -\sqrt{32}[/tex] =
= [tex]\sqrt{2} + \sqrt{2*4} -\sqrt{2*16}[/tex] =
= [tex]\sqrt{2} + \sqrt{2}*\sqrt{4} -\sqrt{2}*\sqrt{16}[/tex] =
= [tex]\sqrt{2} + \sqrt{2}*2 -\sqrt{2}*4[/tex] =
= [tex]\sqrt{2}*(1+2 -4)[/tex] =
= [tex]\sqrt{2}*(-1)[/tex] =
= [tex]-\sqrt{2}[/tex]
b)
[tex]\sqrt{12} - \sqrt{75} +\sqrt{108}[/tex] =
= [tex]\sqrt{3*4} - \sqrt{3*25} +\sqrt{3*36}[/tex] =
= [tex]\sqrt{3}*\sqrt{4} - \sqrt{3}*\sqrt{25} +\sqrt{3}*\sqrt{36}[/tex] =
= [tex]\sqrt{3}*2 - \sqrt{3}*5 +\sqrt{3}*6[/tex] =
= [tex]\sqrt{3}*(2-5+6)[/tex] =
= [tex]\sqrt{3}*3[/tex] =
= [tex]3\sqrt{3}[/tex]
c)
[tex]-2\sqrt{20} +5\sqrt{45} -3\sqrt{125} +4\sqrt{5}[/tex] =
= [tex]-2\sqrt{5*4} +5\sqrt{5*9} -3\sqrt{5*25} +4\sqrt{5}[/tex] =
= [tex]-2\sqrt{5}*\sqrt{4} +5\sqrt{5}*\sqrt{9} -3\sqrt{5}*\sqrt{25} +4\sqrt{5}[/tex] =
= [tex]-2\sqrt{5}*2 +5\sqrt{5}*3 -3\sqrt{5}*5 +4\sqrt{5}[/tex] =
= [tex]-4\sqrt{5} +15\sqrt{5} -15\sqrt{5} +4\sqrt{5}[/tex] =
= [tex]\sqrt{5}*(-4 +15 -15 +4)[/tex] =
= [tex]\sqrt{5}*0[/tex] =
= [tex]0[/tex]
