Question

5.Scoateţi factorii de sub radical: a)√12; b)√20; c)√32; d)√90; e)√120; f)√1000; g)√96; h)√48 ; i)√√98; j)√3200 ; k)√240,1)√8100​

Answer 1

Explicație pas cu pas:

$\sqrt{12} = \sqrt{ {2}^{2} \cdot 3} = 2 \sqrt{3}$

$\sqrt{20} = \sqrt{ {2}^{2} \cdot 5} = 2 \sqrt{5}$

$\sqrt{32} = \sqrt{ {2}^{5} } = {2}^{2} \sqrt{2} = 4 \sqrt{2}$

$\sqrt{90} = \sqrt{ 2 \cdot {3}^{2} \cdot 5} = 3\sqrt{2 \cdot 5} = 3 \sqrt{10}$

$\sqrt{120} = \sqrt{ {2}^{3} \cdot 3 \cdot 5} = 2\sqrt{2 \cdot 3 \cdot 5} = 2 \sqrt{30}$

$\sqrt{1000} = \sqrt{ {2}^{3} \cdot {5}^{3} } = 2 \cdot 5 \sqrt{2 \cdot 5} = 10 \sqrt{10}$

$\sqrt{96} = \sqrt{ {2}^{5} \cdot 3} = {2}^{2} \sqrt{2 \cdot 3} = 4 \sqrt{6}$

$\sqrt{48} = \sqrt{{2}^{4} \cdot 3} = {2}^{2} \sqrt{3} = 4 \sqrt{3}$

$\sqrt{98} = \sqrt{2 \cdot {7}^{2} } = 7 \sqrt{2}$

$\sqrt{3200} = \sqrt{ {2}^{7} \cdot {5}^{2} } = {2}^{3} \cdot 5\sqrt{2} = 40 \sqrt{2}$

$\sqrt{240} = \sqrt{ {2}^{4} \cdot 3 \cdot 5} = {2}^{2} \sqrt{15} = 4 \sqrt{15}$

$\sqrt{ {8}^{100} } = \sqrt{{( {2}^{3} )}^{100}} = \sqrt{ {2}^{300} } = \sqrt{{( {2}^{150} )}^{2}} = {2}^{150}$