Question

Buna. Puteti sa mi rezolvati si mie urmatoarele calcule, dar cu explicatie, va rog? Multumesc!

Answer 1

descompui numerele de sub radical exemplu  $\sqrt{882}=2*3^2*7^2=3*7 \sqrt{2} =21 \sqrt{2}$ apoi extragi de sub radical ce e la puterea 2
a)
$\sqrt{5}(5 \sqrt{3}+2 \sqrt{5}-6 \sqrt{5})+3 \sqrt{5}*4 \sqrt{5}= \\ \sqrt{5}(5 \sqrt{3}-4 \sqrt{5})+60= \\ =3 \sqrt{15}+40$

d)
$2\sqrt{15}(5 \sqrt{6}+8 \sqrt{6}-6 \sqrt{6})-5 \sqrt{10}=2 \sqrt{15}(7 \sqrt{6})-5 \sqrt{10} \\ =14 \sqrt{240}-5 \sqrt{10}$

g)
$16\sqrt{7}( 21 \sqrt{2}+17 \sqrt{2}-13 \sqrt{2}+21 \sqrt{2})=16 \sqrt{7}*46 \sqrt{2}=736 \sqrt{14}$

e)
$12 \sqrt{3}(11 \sqrt{6}-9 \sqrt{6}+7 \sqrt{6}-10 \sqrt{6})+3 \sqrt{10}*8 \sqrt{5}= \\12 \sqrt{3}(-10 \sqrt{6})+24 \sqrt{50}= \\ -120 \sqrt{18}+24 \sqrt{50}=54 \sqrt{6}-360 \sqrt{2}$

f)
$\sqrt{882}( \sqrt{529}- \sqrt{200})+ \sqrt{128}( \sqrt{98}- \sqrt{72)}= \\ 21 \sqrt{2}(23-10 \sqrt{2})+8 \sqrt{2}(7 \sqrt{2}-6 \sqrt{2})= \\ 483 \sqrt{2}-420+16= \\ =483 \sqrt{2}-404$