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# 9.10: Examen de Aptitud

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## Examen de competencia

Para los siguientes problemas, simplifique cada una de las expresiones de raíz cuadrada.

##### Ejercicio$$\PageIndex{1}$$

$$\sqrt{8} \cdot \sqrt{5}$$

Responder

$$2 \sqrt{10}$$

##### Ejercicio$$\PageIndex{2}$$

$$\dfrac{\sqrt{80}}{\sqrt{12}}$$

Responder

$$\dfrac{2 \sqrt{15}}{3}$$

##### Ejercicio$$\PageIndex{3}$$

$$\dfrac{\sqrt{n^2 + n - 12}}{\sqrt{n-3}}$$

Responder

$$\sqrt{n + 4}$$

##### Ejercicio$$\PageIndex{4}$$

$$\sqrt{24a^3b^5c^8}$$

Responder

$$2ab^2c^4 \sqrt{6ab}$$

##### Ejercicio$$\PageIndex{5}$$

$$\sqrt{\dfrac{64x^4y^5z^6}{49a^3b^2c^9}}$$

Responder

$$\dfrac{8x^2y^2z^3\sqrt{acy}}{7a^2bc^5}$$

##### Ejercicio$$\PageIndex{6}$$

$$\sqrt{(x-2)^2(x+1)^4}$$

Responder

$$(x-2)(x+1)^2$$

##### Ejercicio$$\PageIndex{7}$$

$$\sqrt{a^2-8a+16}$$

Responder

$$a-4$$

##### Ejercicio$$\PageIndex{8}$$

$$\dfrac{4}{2 + \sqrt{x}}$$

Responder

$$\dfrac{8 - 4\sqrt{x}}{4 - x}$$

##### Ejercicio$$\PageIndex{9}$$

$$\dfrac{\sqrt{3a}}{\sqrt{2a} + \sqrt{5a}}$$

Responder

$$\dfrac{\sqrt{15} - \sqrt{6}}{3}$$

##### Ejercicio$$\PageIndex{10}$$

$$2x\sqrt{27} + x\sqrt{12}$$

Responder

$$8x\sqrt{3}$$

##### Ejercicio$$\PageIndex{11}$$

$$-3a\sqrt{a^5b^3} + 2a^3b\sqrt{ab}$$

Responder

$$-a^3b\sqrt{ab}$$

##### Ejercicio$$\PageIndex{12}$$

$$\sqrt{10}(\sqrt{8} - \sqrt{2})$$

Responder

$$2\sqrt{5}$$

##### Ejercicio$$\PageIndex{13}$$

$$(3 + \sqrt{6})(2 + \sqrt{5})$$

Responder

$$6 + 3\sqrt{5} + 2\sqrt{6} + \sqrt{30}$$

##### Ejercicio$$\PageIndex{14}$$

$$(\sqrt{10} - \sqrt{3})(\sqrt{5} + \sqrt{2})$$

Responder

$$5\sqrt{2} + 2\sqrt{5} - \sqrt{15} - \sqrt{6}$$

##### Ejercicio$$\PageIndex{15}$$

$$(4 - \sqrt{5y})^2$$

Responder

$$16 - 8\sqrt{5y} + 5y$$

##### Ejercicio$$\PageIndex{16}$$

$$\dfrac{6 - \sqrt{3}}{4 + \sqrt{2}}$$

Responder

$$\dfrac{24 - 6\sqrt{2} - 4\sqrt{3} + \sqrt{6}}{14}$$

##### Ejercicio$$\PageIndex{17}$$

$$\dfrac{\sqrt{2} + \sqrt{3}}{\sqrt{3} - \sqrt{5}}$$

Responder

$$-\dfrac{3 + \sqrt{6} + \sqrt{10} + \sqrt{15}}{2}$$

Para los siguientes problemas, resolver las ecuaciones.

##### Ejercicio$$\PageIndex{18}$$

$$\sqrt{x + 8} = 4$$

Responder

$$x = 8$$

##### Ejercicio$$\PageIndex{19}$$

$$\sqrt{3a + 1} = 4$$

Responder

$$a = 5$$

##### Ejercicio$$\PageIndex{20}$$

$$\sqrt{2x} = -3$$

Responder

Sin solución

##### Ejercicio$$\PageIndex{21}$$

$$\sqrt{3x + 18} + 7 = 0$$

Responder

Sin solución real

##### Ejercicio$$\PageIndex{22}$$

$$\sqrt{3m - 5} = \sqrt{2m + 1}$$

Responder

$$m = 6$$

##### Ejercicio$$\PageIndex{23}$$

$$2\sqrt{a + 2} - 2= 0$$

Responder

$$a = -1$$

##### Ejercicio$$\PageIndex{24}$$

$$\sqrt{b - 7} - \sqrt{5b + 1} = 0$$

Responder

Sin solución

##### Ejercicio$$\PageIndex{25}$$

En una pequeña empresa, el número de ventas mensuales$$S$$ se relaciona aproximadamente con el número de empleados$$E$$ por$$S = 175 + 7\sqrt{E - 3}$$

a) Determinar el número aproximado de ventas si el número de empleados es$$39$$

b) Determinar el número aproximado de empleados si el número de ventas en$$224$$

Responder

a)$$S = 217$$

b)$$E = 52$$

This page titled 9.10: Examen de Aptitud is shared under a CC BY license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .