Question

Me ayudan por xfa con este problema por xfa ​

Answer 1

1)

$3\cdot \sqrt{2}+7\cdot \sqrt{2}-5\cdot \sqrt{2}\\3\sqrt{2}+7\sqrt{2}-5\sqrt{2}$

Luego sumamos los similares:

$=5\sqrt{2}$

2)

$\sqrt{45}-\sqrt{20}+\sqrt{80}-\sqrt{180}$

• $\sqrt{45}=\sqrt{3^2\cdot \:5}=\sqrt{5}\sqrt{3^2}=3\sqrt{5}$
• $\sqrt{20}=\sqrt{2^2\cdot \:5}=\sqrt{5}\sqrt{2^2}=2\sqrt{5}$
• $\sqrt{80}=\sqrt{2^4\cdot \:5}=\sqrt{5}\sqrt{2^4}=2^2\sqrt{5}=4\sqrt{5}$
• $\sqrt{180}=\sqrt{2^2\cdot \:3^2\cdot \:5}=\sqrt{5}\sqrt{2^2}\sqrt{3^2}=2\sqrt{5}\sqrt{3^2}=2\cdot \:3\sqrt{5}=6\sqrt{5}$

$=3\sqrt{5}-2\sqrt{5}+4\sqrt{5}-6\sqrt{5}$

Luego sumamos los similares:

$=-\sqrt{5}$

3)

$\sqrt[3]{54}-\sqrt[3]{250}-\sqrt[3]{16}$

• $\sqrt[3]{54}=\sqrt[3]{3^3\cdot \:2}=\sqrt[3]{2}\sqrt[3]{3^3}=3\sqrt[3]{2}$
• $\sqrt[3]{250}=\sqrt[3]{5^3\cdot \:2}=\sqrt[3]{2}\sqrt[3]{5^3}=5\sqrt[3]{2}$
• $\sqrt[3]{16}=\sqrt[3]{2^4}=\sqrt[3]{2^3\cdot \:2}=\sqrt[3]{2}\sqrt[3]{2^3}=2\sqrt[3]{2}$

$=3\sqrt[3]{2}-5\sqrt[3]{2}-2\sqrt[3]{2}$

Luego sumamos los similares:

$=-4\sqrt[3]{2}$

4)

$2\cdot \sqrt[3]{250}-4\cdot \sqrt[3]{24}-6\cdot \sqrt[3]{16}+\sqrt[3]{2187}\\2\sqrt[3]{250}-4\sqrt[3]{24}-6\sqrt[3]{16}+\sqrt[3]{2187}$

• $2\sqrt[3]{250}=2\cdot \:5\sqrt[3]{2}=10\sqrt[3]{2}$
• $4\sqrt[3]{24}=4\cdot \:2\sqrt[3]{3}=8\sqrt[3]{3}$
• $6\sqrt[3]{16}=6\cdot \:2\sqrt[3]{2}=12\sqrt[3]{2}$
• $\sqrt[3]{2187}=\sqrt[3]{3^7}=\sqrt[3]{3^6\cdot \:3}=\sqrt[3]{3}\sqrt[3]{3^6}=3^2\sqrt[3]{3}=9\sqrt[3]{3}$

$=10\sqrt[3]{2}-8\sqrt[3]{3}-12\sqrt[3]{2}+9\sqrt[3]{3}$

Luego sumamos los similares:

$=-2\sqrt[3]{2}-8\sqrt[3]{3}+9\sqrt[3]{3}\\=-2\sqrt[3]{2}+\sqrt[3]{3}$