Question

$\sqrt{10abc} *\sqrt{15a^{3}c } *\sqrt{12bc}$

Answer 1

Respuesta:

Explicación paso a paso:

Usando las propiedades conocidas de los radicales, la expresión anterior se expresa como:

$\sqrt{10abc}\sqrt{15a^{3}c}\sqrt{12bc}=(10abc)^{1/2}(15a^{3}c)^{1/2}(12bc)^{1/2}$

Realizando los productos y simplificando nos queda:

$(10^{1/2}a^{1/2}b^{1/2}c^{1/2})(15^{1/2}a^{3/2}c^{1/2})(12^{1/2}b^{1/2}c^{1/2})$

$(10^{1/2})(15^{1/2})(12^{1/2})(a^{1/2}a^{3/2})(b^{1/2}b^{1/2})(c^{1/2}c^{1/2}c^{1/2})$

$1800^{1/2}a^{1/2+3/2}b^{1/2+1/2}c^{1/2+1/2+1/2}$

$1800^{1/2}a^{2}bc^{3/2}=\sqrt{1800}a^{2}b\sqrt{c^{3}}$

$30\sqrt{2}a^{2}b\sqrt{c^{3}}$