Question

1. Simplifique os radicais: A)√2²• 5. E)√2⁵• 3³• 5⁶ B)³√2 • 5³. F)√2¹¹• 3⁷• 5 C)⁵√2⁵• 3³. G)⁴√2²¹• 3¹¹ D)⁴√3⁵• 5⁸. H)¹⁰√2⁴³• 5²³. Me ajudem é uma emergência Valendo 28 pontos!!!

Answer 1

Explicação passo-a-passo:

a)

$\sf \sqrt{2^2\cdot5}=\red{2\sqrt{5}}$

b)

$\sf \sqrt[3]{2\cdot5^3}=\red{5\sqrt[3]{2}}$

c)

$\sf \sqrt[5]{2^5\cdot3^3}=2\sqrt[5]{3^3}=\red{2\sqrt[5]{27}}$

d)

$\sf \sqrt[4]{3^5\cdot5^8}$

$\sf =\sqrt[4]{3^4\cdot3\cdot(5^2)^4}$

$\sf =3\cdot5^2\sqrt[4]{3}$

$\sf =3\cdot25\sqrt[4]{3}$

$\sf =\red{75\sqrt[4]{3}}$

e)

$\sf \sqrt{2^5\cdot3^3\cdot5^6}$

$\sf =\sqrt{(2^2)^2\cdot2\cdot3^2\cdot3\cdot(5^3)^2}$

$\sf =2^2\cdot3\cdot5^3\sqrt{2\cdot3}$

$\sf =4\cdot3\cdot125\sqrt{6}$

$\sf =\red{1500\sqrt{6}}$

f)

$\sf \sqrt{2^{11}\cdot3^7\cdot5}$

$\sf =\sqrt{(2^5)^2\cdot2\cdot(3^3)^2\cdot3\cdot5}$

$\sf =2^5\cdot3^3\sqrt{2\cdot3\cdot5}$

$\sf =32\cdot27\sqrt{30}$

$\sf =\red{864\sqrt{30}}$

g)

$\sf \sqrt[4]{2^{21}\cdot3^{11}}$

$\sf =\sqrt[4]{(2^5)^4\cdot2\cdot(3^2)^4\cdot3^3}$

$\sf =2^5\cdot3^2\sqrt[4]{2\cdot3^3}$

$\sf =32\cdot9\sqrt[4]{2\cdot27}$

$\sf =\red{288\sqrt[4]{54}}$

h)

$\sf \sqrt[10]{2^{43}\cdot5^{23}}$

$\sf =\sqrt[10]{(2^4)^{10}\cdot2^3\cdot(5^2)^{10}\cdot5^3}$

$\sf =2^4\cdot5^2\sqrt[10]{2^3\cdot5^3}$

$\sf =16\cdot25\sqrt[10]{8\cdot125}$

$\sf =\red{400\sqrt[10]{1000}}$