Question

Tot nu inteleg cum sa scot de sub radical.

Ex: radical din 432 sau radical din 13824.

Pt un motiv sau altul, nu imi iese.

Answer 1

$a)\sqrt{432} = \\ \\ \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3} = \\ \\ \sqrt{(2 \times 2) \times (2 \times 2) \times (3 \times 3) \times 3} = \\ \\ \sqrt{ {2}^{2} \times {2}^{2} \times {3}^{2} \times 3 } = \\ \\ (2 \times 2 \times 3) \sqrt{3} = \\ \\ 12 \sqrt{3}$

$b) \sqrt{13824} = \\ \\ \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3} = \\ \\ \sqrt{(2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times 3} = \\ \\ \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} \times {2}^{2} \times {3}^{2} \times 2 \times 3 } = \\ \\ (2 \times 2 \times 2 \times 2 \times 3) \sqrt{2 \times 3} = \\ \\ 48 \sqrt{6}$

Answer 2

Răspuns:

Explicație pas cu pas:

Trebuie sa descompui in factori primi, daca nu folosesti metoda clasica.

√432=√2^4×3³=2²×3×√3=12√3

√13824=√2^5×432=√2^9×3³=2^4×3×√6=48√6     (√3 aprox 1,73)