Question

5-Simplifique as seguintes raízes:
a)
$\sqrt[4]{112}$
b)
$\sqrt{500}$

c)
$\sqrt[4]{800}$
​

Answer 1

Explicação passo-a-passo:

$\sqrt[4]{112} \\ 112 \div 2 = 56 \\ 56 \div 2 = 28 \\ 28 \div 2 = 14 \\ 14 \div 2 = 7 \\ 7 \div 7 = 1 \\ \sqrt[4]{112} = \sqrt[4]{2 {}^{4 \times 7} } \\ \sqrt[4]{112} = 2 \sqrt[4]{7}$

$\sqrt{500} \\500 \div 2 = 250 \\ 250 \div 2 = 125 \\ 125 \div 5 = 25 \\ 25 \div 5 = 5 \\ 5 \div 5 = 1 \\ \sqrt{500} = \sqrt{2 {}^{2} \times 5 {}^{2} \times 5 } \\ \sqrt{500} = 2 \times 5 \sqrt{5} \\ \sqrt{500} = 10 \sqrt{5}$

$\sqrt[4]{800} \\ 800 \div 2 = 400 \\ 400 \div 2 = 200 \\ 200 \div 2 = 100 \\ 100 \div 2 = 50 \\ 50 \div 2 = 25 \\ 25 \div 5 = 5 \\ 5 \div 5 = 1 \\ \sqrt[4]{800} = \sqrt[4]{ 2 {}^{4 \times 2 \times 5 {}^{2} } } \\ \sqrt[4]{800} = 2 \sqrt[4]{2 \times 25} = 2 \sqrt[4]{50} \\ \sqrt[4]{800} = 2 \sqrt[4]{50}$