Question

section 1.3: i will be able to simplify radical expressions. simplify each expression. show your work and circle the final answer.

1. \\(\sqrt{125})
2. \\(5\sqrt{98})
3. \\(\sqrt{196x^{4}y^{14}})
4. \\(- 3\sqrt{448})
5. \\(\sqrt{\frac{12}{169}}\cdot7\\)

6.

1. \\(\sqrt{\frac{147}{32}}\\)

8.

1. \\(\frac{6\sqrt{3}}{\sqrt{7}}\\)

Explanation:

Step1: Simplificar $\sqrt{125}$

Descomponemos 125 en factores primos: $125 = 5\times5\times5$. Entonces $\sqrt{125}=\sqrt{5^{2}\times5}=5\sqrt{5}$.

Step2: Simplificar $5\sqrt{98}$

Descomponemos 98 en factores primos: $98 = 2\times7\times7$. Entonces $5\sqrt{98}=5\sqrt{2\times7^{2}} = 5\times7\sqrt{2}=35\sqrt{2}$.

Step3: Simplificar $\sqrt{196x^{4}y^{14}}$

Sabemos que $196 = 14\times14$, entonces $\sqrt{196x^{4}y^{14}}=\sqrt{14^{2}(x^{2})^{2}(y^{7})^{2}} = 14x^{2}y^{7}$.

Step4: Simplificar $- 3\sqrt{48b^{3}}$

Descomponemos 48 en factores primos: $48=2\times2\times2\times2\times3$. Y $b^{3}=b^{2}\times b$. Entonces $-3\sqrt{48b^{3}}=-3\sqrt{2^{4}\times3\times b^{2}\times b}=-3\times4b\sqrt{3b}=-12b\sqrt{3b}$.

Step5: Simplificar $\sqrt{\frac{121}{169}}$

$\sqrt{\frac{121}{169}}=\frac{\sqrt{121}}{\sqrt{169}}=\frac{11}{13}$.

Step6: Simplificar $\frac{\sqrt{192}}{\sqrt{12}}$

$\frac{\sqrt{192}}{\sqrt{12}}=\sqrt{\frac{192}{12}}=\sqrt{16} = 4$.

Step7: Simplificar $\frac{\sqrt{60}}{\sqrt{5}}$

$\frac{\sqrt{60}}{\sqrt{5}}=\sqrt{\frac{60}{5}}=\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}$.

Step8: Simplificar $\frac{6\sqrt{8}}{\sqrt{2}}$

$\frac{6\sqrt{8}}{\sqrt{2}}=6\sqrt{\frac{8}{2}}=6\sqrt{4}=6\times2 = 12$.

Answer:

1. $5\sqrt{5}$
2. $35\sqrt{2}$
3. $14x^{2}y^{7}$
4. $-12b\sqrt{3b}$
5. $\frac{11}{13}$
6. 4
7. $2\sqrt{3}$
8. 12