Question

calcule o valor das expressões a)(2√18+5√72-3√50) : (7√2)
b) (√20-√45+√80) . (2√5+√180)
c) (2√27-2√12) . (4*√3√7)​

Answer 1

a) $\frac{(2\sqrt{18}+5\sqrt{72}-3\sqrt{50})}{(7\sqrt{2})}$

Fatorar as raízes em fatores primos

18 I 2

9  I 3   3².2 = 3√2

3  I 3

1

72 I 2

36 I 2

18  I 2  2.2².3² = 3.2√2 = 6√2

9   I 3

3   I 3

1

50 I 2

25 I 5   2.5² = 5√2

5   I 5

1

$\frac{(2.3\sqrt{2} + 5.6\sqrt{2}-3.5\sqrt{2}  }{7\sqrt{2} } \\ \\ \frac{6\sqrt{2}+30\sqrt{2}-15\sqrt{2}   }{7\sqrt{2} } \\ \\ \frac{21\sqrt{2} }{7\sqrt{2} } \\ \\ \\ 3\sqrt{2}$

b) $(\sqrt{20} -\sqrt{45} +\sqrt{80} ).(2\sqrt{5} +\sqrt{180} )$

20 I 2

10  I 2   2².5 = 2√5

5   I 5

1

45 I 3

15  I 3  3².5 = 3√5

5   I 5

1

80 I 2

40 I 2

20 I 2   2².2².5 = 2.2√5 = 4√5

10  I 2

5   I 5

1

180 I 2

90  I 2

45  I 3   2².3².5 = 2.3√5 = 6√5

15  I 3

5   I 5

1

$(2\sqrt{5} -3\sqrt{5} +4\sqrt{5} ).(2\sqrt{5} +6\sqrt{5} )\\ \\ 3\sqrt{5} . 8\sqrt{5} \\ \\ 24\sqrt{25} \\ \\ 24.5\\ \\ 120$

c) $(2\sqrt{27} -2\sqrt{12} ).(4\sqrt{3} \sqrt{7})$

27 I 3

9   I 3  3².3 = 3√3

3   I 3

1

12 I 2

6  I 2  2².3 = 2√3

3  I 3

1

$(2.3\sqrt{3} -2.2\sqrt{3} ).(4\sqrt{3} .\sqrt{7} )\\ \\ (6\sqrt{3} -4\sqrt{3} ).(4\sqrt{27}) \\ \\ (6\sqrt{3} -4\sqrt{3} ).(4.3\sqrt{3} )\\ \\ 2\sqrt{3} .12\sqrt{3} \\ \\ 24\sqrt{9} \\ \\ 24.3\\ \\ 72$