Question

soma algébrica 3✓1250+✓85-✓128​

Answer 1

Resposta:

Explicação passo-a-passo:

Fatores os números que estão na raiz:

1250, 1 | 2

625, 1 | 5

125, 1 | 5

25, 1 | 5

5, 1 | 5

1, 1 | 1 /

1250=2.5^4

85, 1 | 5

17, 1 | 17

1, 1 | 1/

85=5.17

128, 1 | 2

64, 1 | 2

32, 1 | 2

16, 1 | 2

8, 1 | 2

4, 1 | 2

2, 1 | 2

1, 1 | 1

128=2^7

$3\sqrt{1250} +\sqrt{85} -\sqrt{128} =3\sqrt{2.5^{4}} +\sqrt{5.17} -\sqrt{2^{7}} =3.(2^{1}.5^{4})^{\frac{1}{2}}+\sqrt{5.17}-(2^{7})^{\frac{1}{2}} =3.(2^{\frac{1}{2} }.5^{\frac{4}{2}})+\sqrt{5.17}-(2)^{\frac{7}{2}}=3.25.2^{\frac{1}{2} }+\sqrt{5.17}-(2)^{(\frac{6}{2}+\frac{1}{2} )}=75.2^{\frac{1}{2} }+\sqrt{5.17}-(2^{\frac{6}{2}}.2^{\frac{1}{2}})=75\sqrt{2} +\sqrt{5.17}-2^{3}.2^{\frac{1}{2} }=75\sqrt{2} +\sqrt{5.17}-8\sqrt{2} =67\sqrt{2} +\sqrt{85}$

Propriedades:

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$