Question

= Scoateţi factori de sub radical şi apoi calculați: a) V2 +V8-V32 b) V12 – V75 +V 108 c) -2V20+5V45 – 3V125 +4V5 = ? V este radical .​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

$\sqrt{2} + \sqrt{8} -\sqrt{32}$ =  

= $\sqrt{2} + \sqrt{2*4} -\sqrt{2*16}$ =

= $\sqrt{2} + \sqrt{2}*\sqrt{4} -\sqrt{2}*\sqrt{16}$ =

= $\sqrt{2} + \sqrt{2}*2 -\sqrt{2}*4$ =

= $\sqrt{2}*(1+2 -4)$ =

= $\sqrt{2}*(-1)$ =

= $-\sqrt{2}$

b)

$\sqrt{12} - \sqrt{75} +\sqrt{108}$ =  

= $\sqrt{3*4} - \sqrt{3*25} +\sqrt{3*36}$ =

= $\sqrt{3}*\sqrt{4} - \sqrt{3}*\sqrt{25} +\sqrt{3}*\sqrt{36}$ =

= $\sqrt{3}*2 - \sqrt{3}*5 +\sqrt{3}*6$ =

= $\sqrt{3}*(2-5+6)$ =

= $\sqrt{3}*3$ =

= $3\sqrt{3}$

c)

$-2\sqrt{20} +5\sqrt{45} -3\sqrt{125} +4\sqrt{5}$ =

= $-2\sqrt{5*4} +5\sqrt{5*9} -3\sqrt{5*25} +4\sqrt{5}$ =

= $-2\sqrt{5}*\sqrt{4} +5\sqrt{5}*\sqrt{9} -3\sqrt{5}*\sqrt{25} +4\sqrt{5}$ =

= $-2\sqrt{5}*2 +5\sqrt{5}*3 -3\sqrt{5}*5 +4\sqrt{5}$ =

= $-4\sqrt{5} +15\sqrt{5} -15\sqrt{5} +4\sqrt{5}$ =

= $\sqrt{5}*(-4 +15 -15 +4)$ =

= $\sqrt{5}*0$ =

= $0$