Question

simplifique através da fatoração:
a)³√250=
b)√192=
c)³√375=
d)⁴√176​

Answer 1

$a) \\ \\ \sqrt[3]{250} = \sqrt[3]{5 {}^{2} \times 10 } = \sqrt[3]{5 {}^{2} \times( 2 \times 5)} \\ \\ = \sqrt[3]{5 {}^{3} \times 2 } \\ \\ = 5 \sqrt[3]{2}$

$b) \\ \sqrt{192} = \sqrt{96 \times 2} = \sqrt{48 \times 4} \\ \\ = \sqrt{8 \times 6 \times 4 } \\ = \sqrt{8 \times 2 \times 3 \times 4} \\ = \sqrt{2 {}^{3} \times 2 \times 3 \times 2 {}^{2} } \\ = \sqrt{2 {}^{6} \times 3} \\ = 8 \sqrt{3}$

$c) \\ \sqrt[3]{375} = \sqrt[3]{5 \times 75} = \sqrt[3]{5 \times 25 \times 3} \\ = \sqrt[3]{5 {}^{3} \times 3} \\ = 5 \sqrt[3]{3}$

$d) \\ \sqrt[4]{176} = \sqrt[4]{88 \times 2} = \sqrt[4]{11 \times 8 \times 2} \\ \\ = \sqrt[4]{11 \times 2 {}^{4} } \\ = 2\sqrt[4]{11}$