▶️ Ejercicio 240 álgebra - Solucionario Baldor ✅✅

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CAPITULO XXXI

R a d i c a l e s
Multiplicación de radicales del mismo índice

Ejercicio 240

Multiplicar:

$\sqrt{3} \times \sqrt{6} = \sqrt{3 \times 6} = \sqrt{18} = \sqrt{3^{2} \times 2} = 3 \sqrt{2}$
$5 \sqrt{21} \times 2 \sqrt{3} = 5 \times 2 \sqrt{21 \times 3} = 10 \sqrt{63} = 10 \sqrt{7 \times 3^{2}} = 10 \times 3 \sqrt{7} = 30 \sqrt{7}$
$\frac{1}{2} \sqrt{14} \times \frac{2}{7} \sqrt{21} = \frac{1}{2} \times \frac{2}{7} \sqrt{14 \times 21} = \frac{1}{7} \sqrt{7 \times 2 \times 7 \times 3} = \frac{1}{7} \sqrt{7^{2} \times 6} = \frac{1}{7} . 7 \sqrt{6} = \sqrt{6}$
$\sqrt[3]{12} \times \sqrt[3]{9} = \sqrt[3]{2^{2} \times 3 \times 3^{2}} = \sqrt[3]{2^{2} \times 3^{3}} = 3 \sqrt[3]{4}$
$\frac{5}{6} \sqrt[3]{15} \times 12 \sqrt[3]{50} = \frac{5}{6} \times \sqrt[3]{3 \times 5 \times 5^{2} \times 2} = 10 \sqrt[3]{6 \times 5^{3}} = 10 \times 5 \sqrt[3]{6} = 50 \sqrt[3]{6}$
$x \sqrt{2 a} \times \frac{1}{a} \sqrt{5 a} = x \times \frac{1}{a} \sqrt{2 a \times 5 a} = \frac{x}{a} \sqrt{10 a^{2}} = \frac{x}{a} \times a \sqrt{10} = x \sqrt{10}$
$5 \sqrt{12} \times 3 \sqrt{75} = 5 \times 3 \sqrt{3 \times 2^{2} \times 5^{2} \times 3} = 15 \sqrt{3^{2} \times 2^{2} \times 5^{2}} = 15 \times 2 \times 3 \times 5 = 450$
$\frac{3}{4} \sqrt[3]{9 a^{2}} \times 8 \sqrt[3]{3 a b} = \frac{3}{4} \times \sqrt[3]{3^{2} a^{2} \times 3 a b} = 6 \sqrt[3]{3^{3} a^{3} b} = 6 \times 3 a \sqrt[3]{b} = 18 a \sqrt[3]{b}$
$3 \sqrt{6} \times \sqrt{14} \times 2 \sqrt{35} = 3 \times 2 \sqrt{2 \times 3 \times 2 \times 7 \times 7 \times 5} = 6 \sqrt{2^{2} \times 3 \times 7^{2} \times 5} = 6 \times 2 \times 7 \sqrt{15} = 84 \sqrt{15}$

Categories: Capítulo XXXI