Propiedad de la radicación 1: Según la propiedad ¿Cuál de las opciones son las correctas? $$\sqrt[n]{x\cdot y\ }\ =\sqrt[n]{x}\ \cdot\ \sqrt[n]{y}$$ y a la inversa, $$\sqrt[n]{x}\ \cdot\ \sqrt[n]{y}\ =\ \sqrt[n]{x\cdot y}$$ Entonces ¿Cuál es la respuesta de...? $$\sqrt[3]{\left(3\right)\left(5\right)}$$ y $$\sqrt[3]{3}\cdot\ \sqrt[3]{5}$$

$$\sqrt[3]{\left(3\right)\left(5\right)}=\sqrt[3]{3}\cdot\sqrt[3]{5}$$ y $$\sqrt[3]{3}\cdot\ \sqrt[3]{5}\ =\ \sqrt[3]{\left(3\right)\left(5\right)}$$

$$\sqrt[3]{\left(3\right)\left(5\right)}=\sqrt[3]{3}\cdot\sqrt[3]{5}$$ y $$\sqrt[2]{3}\cdot\sqrt[3]{5}\ =\sqrt[3]{\left(3\right)\left(5\right)}$$

$$\sqrt[3]{3\cdot5}=\sqrt[3]{3}\cdot\sqrt[3]{2}$$ y $$\sqrt[3]{3}\cdot\sqrt[3]{5}\ =\sqrt[3]{3\cdot5}$$

$$\sqrt[2]{3\cdot5}=\sqrt[3]{3}\cdot\sqrt[5]{2}$$ y $$\sqrt[2]{3}\cdot\sqrt[3]{5}\ =\sqrt[5]{3\cdot5}$$

Propiedad de la radicación 3: $$\sqrt[m]{\sqrt[n]{a}\ }\ =\ \ \sqrt[m\cdot n]{a}$$ Resuelve, $$\sqrt[7]{\sqrt[4]{5}}$$

$$\sqrt[7\cdot4]{5}=\sqrt[28]{5}$$ .

$$\sqrt[7\cdot3]{5}=\sqrt[27]{5}$$ .

$$\sqrt[7\cdot5]{5}=\sqrt[28]{5}$$ .

$$\sqrt[7\cdot5]{5}=\sqrt[15]{5}$$ .

Simplificación III: Exponentes, $$2^5=2\cdot2\cdot2\cdot2\cdot2\ =32$$ En una raíz, $$\sqrt[2]{2^5}=$$ , el índice ( $$\sqrt[2]{}$$ ) buscamos sus múltiplos (mult de dos: 2, 4, 6, 8, 10...). $$2^5=2\cdot2\cdot2\cdot2\cdot2$$ buscamos la cantidad que puede agarrar los múltiplos de dos en este caso solo 4, si escogemos 6 nos faltará uno. Lo que nos queda lo siguiente; $$2^4\cdot2^1$$ y se pasa a raíz y aplicamos la propiedad. $$\sqrt[2]{2^4\cdot2^1}=\ \sqrt[]{2^4}\cdot\sqrt[]{2^1}$$ , aplicamos simplificación si se puede, $$\sqrt[]{2^4}=2^2\cdot\sqrt[]{2^1}=4\sqrt[]{2}$$ lo cual el resultado lo sabremos cuando el radicando tenga un exponente menor que el de la raíz. Resuelve: $$\sqrt[5]{4^{17}}$$

$$\sqrt[5]{4^{17}}=\sqrt[5]{4^{12}}\cdot\sqrt[5]{4^5}$$ Simplificamos $$4^3\cdot\sqrt[5]{4^2}=32\cdot\sqrt[5]{4^2}$$

$$\sqrt[5]{4^{17}}=\sqrt[5]{4^{15}}\cdot\sqrt[5]{4^2}$$ Simplificamos $$4^3\cdot\sqrt[5]{4^2}=32\cdot\sqrt[5]{4^2}$$

$$\sqrt[5]{4^{15}}=\sqrt[5]{4^{15}}\cdot\sqrt[5]{4^2}$$ Simplificamos $$4^3\cdot\sqrt[5]{4^2}=34\cdot\sqrt[5]{4^2}$$

Repaso Raices

Quiz

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

Alejandro Duque

Used 2+ times

FREE Resource

8 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

a es el índice

v es el radicando

c es la base

a es el índice

v es el radicando

c es el coeficiente

a es el coeficiente

v es el índice

c es el radicando

a es el radicando

v es el coeficiente

c es el índice

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

3.

MULTIPLE SELECT QUESTION

2 mins • 1 pt

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

6.

MULTIPLE SELECT QUESTION

1 min • 1 pt

7.

MULTIPLE SELECT QUESTION

1 min • 1 pt

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