Question

scoateti factori de sub radical:√8,√12,√18,√20,√24,√27,√28,√32,√40,√44,√48,√45,√50,√52

Answer 1

Răspuns

Explicație pas cu pas:

√8 = √4 × √ 2 = 2√2

√12 = √(4×3) = 2√3

√18 = √(9×2) = 3√2

√20 = √(4×5) = 2√5

√24 = √(4×6) = 2√6

√27 = √(9×3) = 3√3 ;     √9 = 3

√28 = √(2²×7) = 2√7

√32 = √(4²×2) = 4√2

√40 = √(4×10) = 2√10

√44 = √(4×11) = 2√11

√48 = √(16×3) = 4√3

√45 = √(9×5) = 3√5

√50= √(5²×2) = 5√2

√52 = √(2²×13) = 2√13

Answer 2

$a) \sqrt{8} = \sqrt{2 \times 2 \times 2} = \sqrt{(2 \times 2) \times 2} = \sqrt{ {2}^{2} \times 2 } = 2 \sqrt{2}$

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

$c) \sqrt{18} = \sqrt{2 \times 3 \times 3} = \sqrt{(3 \times 3) \times 2} = \sqrt{ {3}^{2} \times 2 } = 3 \sqrt{2}$

$d) \sqrt{20} = \sqrt{2 \times 2 \times 5} = \sqrt{(2 \times 2) \times 5} = \sqrt{ {2}^{2} \times 5 } = 2 \sqrt{5}$

$e) \sqrt{24} = \sqrt{2 \times 2 \times 2 \times 3} = \sqrt{(2 \times 2) \times 2 \times 3} = \sqrt{ {2}^{2} \times 2 \times 3 } = 2 \sqrt{2 \times 3} = 2 \sqrt{6}$

$f) \sqrt{27} = \sqrt{3 \times 3 \times 3} = \sqrt{(3 \times 3) \times 3} = \sqrt{ {3}^{2} \times 3 } = 3 \sqrt{3}$

$g) \sqrt{28} = \sqrt{2 \times 2 \times 7} = \sqrt{(2 \times 2) \times 7} = \sqrt{ {2}^{2} \times 7 } = 2 \sqrt{7}$

$h) \sqrt{32} = \sqrt{2 \times 2 \times 2 \times 2 \times 2} = \sqrt{(2 \times 2) \times (2 \times 2) \times 2} = \sqrt{ {2}^{2} \times {2}^{2} \times 2 } = (2 \times 2) \sqrt{2} = 4 \sqrt{2}$

$i) \sqrt{40} = \sqrt{2 \times 2 \times 2 \times 5} = \sqrt{(2 \times 2) \times 2 \times 5} = \sqrt{ {2}^{2} \times 2 \times 5 } = 2 \sqrt{2 \times 5} = 2 \sqrt{10}$

$j) \sqrt{44} = \sqrt{2 \times 2 \times 11} = \sqrt{(2 \times 2) \times 11} = \sqrt{ {2}^{2} \times 11 } = 2 \sqrt{11}$

$k) \sqrt{48} = \sqrt{2 \times 2 \times 2 \times 2 \times 3} = \sqrt{(2 \times 2) \times (2 \times 2) \times 3} = \sqrt{ {2}^{2} \times {2}^{2} \times 3 } = (2 \times 2) \sqrt{3} = 4 \sqrt{3}$

$l) \sqrt{45} = \sqrt{3 \times 3 \times 5} = \sqrt{(3 \times 3) \times 5} = \sqrt{ {3}^{2} \times 5 } = 3 \sqrt{5}$

$m) \sqrt{50} = \sqrt{2 \times 5 \times 5} = \sqrt{(5 \times 5) \times 2} = \sqrt{ {5}^{2} \times 2 } = 5 \sqrt{2}$

$n) \sqrt{52} = \sqrt{2 \times 2 \times 13} = \sqrt{(2 \times 2) \times 13} = \sqrt{ {2}^{2} \times 13 } = 2 \sqrt{13}$