▶️ Ejercicio 255 álgebra - Solucionario Baldor ✅✅

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CAPITULO XXXII

CANTIDADES IMAGINARIAS

Ejercicio 255

Multiplicar

$\begin{matrix} \sqrt{- 16} \times \sqrt{- 25} & = \sqrt{(- 1) (4^{2})} \times \sqrt{(- 1) (5^{2})} \\ = 4 \sqrt{- 1} \times 5 \sqrt{(- 1) 5} \\ = 20 {(\sqrt{- 1})}^{2} \\ = - 20 \end{matrix}$
$\begin{matrix} \sqrt{- 81} \times \sqrt{- 49} & = \sqrt{(- 1) (9^{2})} \times \sqrt{(- 1) (7^{2})} \\ = 9 \sqrt{- 1} \times 7 \sqrt{- 1} \\ = 63 {(\sqrt{- 1})}^{2} \\ = - 63 \end{matrix}$
$\begin{matrix} 5 \sqrt{- 36} \times 4 \sqrt{- 64} & = 5 \sqrt{(- 1) (6^{2})} \times 4 \sqrt{(- 1) (8^{2})} \\ = 5 \times 6 \sqrt{- 1} \times 4 \times 8 \sqrt{- 1} \\ = 960 {(\sqrt{- 1})}^{2} \\ = - 960 \end{matrix}$
$\begin{matrix} \sqrt{- 3} \times \sqrt{- 2} & = \sqrt{(- 1) (3)} \times \sqrt{(- 1) (2)} \\ = 3 \sqrt{- 1} \times 2 \sqrt{- 1} \\ = 6 {(\sqrt{- 1})}^{2} \\ = - 6 \end{matrix}$
$\begin{matrix} 2 \sqrt{- 5} \times 3 \sqrt{- 7} & = 2 \sqrt{(- 1) (5)} \times 3 \sqrt{(- 1) (7)} \\ = 2 \sqrt{- 1} \sqrt{5} \times 3 \sqrt{- 1} \sqrt{7} \\ = 6 \sqrt{35} {(\sqrt{- 1})}^{2} \\ = - 6 \sqrt{35} \end{matrix}$
$\begin{matrix} \sqrt{- 3} \times \sqrt{- 75} & = \sqrt{(- 1) (3)} \times \sqrt{(- 1) (3) (5^{2})} \\ = \sqrt{- 1} \sqrt{3} \times 5 \sqrt{- 1} \sqrt{3} \\ = 5 {(\sqrt{- 1})}^{2} {(\sqrt{3})}^{2} \\ = - 15 \end{matrix}$
$\begin{matrix} 2 \sqrt{- 7} \times 3 \sqrt{- 28} & = 2 \sqrt{(- 1) (7)} \times 3 \sqrt{(- 1) (2^{2}) (7)} \\ = 2 \sqrt{- 1} \sqrt{7} \times 3 \times 2 \sqrt{- 1} \sqrt{7} \\ = 12 {(\sqrt{- 1})}^{2} {(\sqrt{7})}^{2} \\ = - 84 \end{matrix}$
$\begin{matrix} \sqrt{- 49} \times \sqrt{- 4} \times \sqrt{- 9} & = \sqrt{(- 1) (7^{2})} \times \sqrt{(- 1) (2^{2})} \times \sqrt{(- 1) (3^{2})} \\ = 7 \sqrt{- 1} \times 2 \sqrt{- 1} \times 3 \sqrt{- 1} \\ = 42 {(\sqrt{- 1})}^{3} \\ = 42 {(\sqrt{- 1})}^{2} (\sqrt{- 1}) \\ = - 42 i \end{matrix}$
$\begin{matrix} \sqrt{- 2} \times 3 \sqrt{- 5} \times \sqrt{- 10} & = \sqrt{(- 1) (2)} \times 3 \sqrt{(- 1) (5)} \times \sqrt{(- 1) (5) (2)} \\ = \sqrt{- 1} \sqrt{2} \times 3 \sqrt{- 1} \sqrt{5} \times \sqrt{- 1} \sqrt{5} \sqrt{2} \\ = 3 {(\sqrt{- 1})}^{3} {(\sqrt{5})}^{2} {(\sqrt{2})}^{2} \\ = 3 (5) (2) {(\sqrt{- 1})}^{2} (\sqrt{- 1}) \\ = - 30 i \end{matrix}$
$\begin{matrix} \sqrt{- 12} \times \sqrt{- 27} \times \sqrt{- 8} \times \sqrt{- 50} & = \sqrt{(- 1) (2^{2}) (3)} \times \sqrt{(- 1) (3^{2}) (3)} \times \sqrt{(- 1) (2^{2}) (2)} \times \sqrt{(- 1) (5^{2}) (2)} \\ = 2 \sqrt{- 1} \sqrt{3} \times 3 \sqrt{- 1} \sqrt{3} \times 2 \sqrt{- 1} \sqrt{2} \times 5 \sqrt{- 1} \sqrt{2} \\ = 2 \times 3 \times 2 \times 5 {(\sqrt{3})}^{2} {(\sqrt{2})}^{2} \\ = 60 (3) (2) \\ = 360 \end{matrix}$
$\begin{matrix} - 5 \sqrt{- x} \times 3 \sqrt{- y} & = - 5 \sqrt{(- 1) (x)} \times 3 \sqrt{(- 1) (y)} \\ = - 5 \sqrt{- 1} \sqrt{x} \times 3 \sqrt{- 1} \sqrt{y} \\ = 15 {(\sqrt{- 1})}^{2} \sqrt{x y} \\ = - 15 \sqrt{x y} \end{matrix}$

Categories: Capítulo XXXII