Question

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Answer 1

Răspuns:

a)

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

$3 \sqrt{242} = 3 \sqrt{2 \times {11}^{2} } = 33 \sqrt{2}$

$5 \sqrt{32} = 5 \sqrt{ {2}^{5} } = 20 \sqrt{2}$

$3 \sqrt{50} = 3 \sqrt{2 \times {5}^{2} } = 15 \sqrt{2}$

$2 \sqrt{128} = 2 \sqrt{ {2}^{7} } = 16 \sqrt{2}$

$7 \sqrt{2} (33 \sqrt{2} - 20 \sqrt{2} + 15 \sqrt{2} - 16 \sqrt{2} ) = 7 \sqrt{2} \times 12 \sqrt{2} = 168$

b)

$\sqrt{125} = \sqrt{ {5}^{3} } = 5 \sqrt{5}$

$2 \sqrt{27} = 2 \sqrt{ {3}^{3} } = 6 \sqrt{3}$

$5 \sqrt{48} = 5 \sqrt{ {2}^{4} \times 3} = 20 \sqrt{3}$

$3 \sqrt{147} = 3 \sqrt{3 \times {7}^{2} } = 21 \sqrt{3}$

$9 \sqrt{300} = 9 \sqrt{ {2}^{2} \times 3 \times {5}^{2} } = 90 \sqrt{3}$

$5 \sqrt{5} (6 \sqrt{3} - 20 \sqrt{3} - 21 \sqrt{3} + 90 \sqrt{3} ) = 5 \sqrt{5} \times 55 \sqrt{3} = 275 \sqrt{15}$

c)

$\sqrt{112} = \sqrt{ {2}^{4} \times 7 } = 4 \sqrt{7}$

$3 \sqrt{288} = 3 \sqrt{2 \times {12}^{2} } = 36 \sqrt{2}$

$2 \sqrt{648} = 2 \sqrt{ {2}^{3} \times {3}^{4} } = 36 \sqrt{2}$

$2 \sqrt{847} = 2 \sqrt{7 \times {11}^{2} } = 22 \sqrt{7}$

$3 \sqrt{4375} = 3 \sqrt{ {5}^{4} \times 7 } = 75 \sqrt{7}$

$4 \sqrt{7} (36 \sqrt{2} + 36 \sqrt{2} ) - 18 \sqrt{2} (22 \sqrt{7} - 75 \sqrt{7} ) = 288 \sqrt{14} + 954 \sqrt{14} = 1242 \sqrt{14}$