Question

AYUDA por favor es para mañana ​

Answer 1

Respuesta:

$a) \sqrt[3]{2^{10}} =\\\\\sqrt[3]{2 * 2 * 2 *2 *2 *2 *2 *2 *2 *2} = \sqrt[3]{2^3 * 2^3 * 2^3 * 2}\\\\\sqrt[3]{2^3}* \sqrt[3]{2^3}* \sqrt[3]{2^3} *\sqrt[3]{2} = 2 * 2 *2 *\sqrt[3]{2} = 8\sqrt[3]{2}$

$b) \sqrt{3^5}= \\\\\sqrt{3 * 3 * 3 * 3 *3} = \sqrt{3^2 * 3^2 * 3} = \sqrt{3^2}* \sqrt{3^2} *\sqrt{3} = 3 * 3 *\sqrt{3} = 9\sqrt{3}$

$c) \sqrt[5]{3^{15}} =\\\\3^{15*\frac{1}{5} } = 3^{\frac{15}{5} } = 3^3 = 27$

$d) \sqrt{x^{10}} =\\\\x^{10*\frac{1}{2} } = x^{\frac{10}{2} } = x^5$

$e)\sqrt{12} = \\\\\sqrt{4*3}= \sqrt{4}* \sqrt{3} = \sqrt{2^2} * \sqrt{3} = 2\sqrt{3}$

$f) \sqrt{256} =\\\\\sqrt{16 * 16} = \sqrt{16} *\sqrt{16} = \sqrt{4^2} * \sqrt{4^2} = 4 * 4 = 16$

$g) \sqrt{9x^3} =\\\\ \sqrt{9 *x^3} = \sqrt{9}* \sqrt{x^3} = \sqrt{3^2}* \sqrt{x^2 * x} = 3 * \sqrt{x^2}* \sqrt{x} = 3 *x *\sqrt{x} = 3x\sqrt{x}$

$h)\sqrt[3]{54a^2} =\\\\\sqrt[3]{2a * 3a * 3a * 3a} = \sqrt[3]{(3a)^3 * 2a} = \sqrt[3]{(3a)^3} * \sqrt[3]{2a} = 3a\sqrt[3]{2a}$

Explicación paso a paso: