Question

Aduceti la forma cea mai simpla expresia
8√48-8√80+5√405-7√147

Answer 1

Răspuns:

Aduceti la forma cea mai simpla expresia  .

Pentru aceasta vom scoate factorii de sub radical .

8√48 - 8√80 + 5√405 - 7√147 =

$\displaystyle 8\sqrt{16 \cdot 3} \ - \ 8\sqrt{16 \cdot\ 5} \ + \ 5\sqrt{81 \cdot\ 5} - \ 7\sqrt{49 \cdot\ 3} = \\\\\displaystyle 8\sqrt{4^{2} \cdot 3} \ - \ 8\sqrt{4^{2} \cdot\ 5} \ + \ 5\sqrt{9^{2} \cdot\ 5} - \ 7\sqrt{7^{2} \cdot\ 3} = \\\\\\\displaystyle 8 \ \cdot \ 4 \sqrt{3 } \ - 8 \ \cdot \ 4\sqrt{5} \ + \ 5 \ \cdot \ 9\sqrt{5} \ - 7 \ \cdot \ 7 \sqrt{3} \ = \\ \\\displaystyle 32\sqrt{3} \ - \ 32\sqrt{5} \ + \ 45\sqrt{5} \ - 49\sqrt{3} =$

$\displaystyle 32\sqrt{3} \ - \ 49\sqrt{3} \ - \ 32\sqrt{5} \ + \ 45 \sqrt{5} \ = \\ \\\displaystyle \ - \ 17\sqrt{3} \ + 13\sqrt{5} \ = \\ \\\displaystyle \boxed{13\sqrt{5} \ - \ 17 \sqrt{3} }$