Podrian ayudarme a resolver, si pueden explicarme tambien, se los agradeceria.
Adjuntos:
![](https://es-static.z-dn.net/files/df1/b91fc72e95fec1c98613f7f44d5fb0cb.jpg)
Granpez:
solo es reduccion verdad?
Respuestas
Respuesta dada por:
2
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Adjuntos:
![](https://es-static.z-dn.net/files/d01/0050d642610721ecfc501308f9f91a53.jpg)
![](https://es-static.z-dn.net/files/d6a/88461afe6de87a5dd85cd103491a4dcc.jpg)
Respuesta dada por:
2
1)
![5 \sqrt{8} -3 \sqrt{2} + \sqrt{5} +5 \sqrt{32} -4 \sqrt{5} = \\ \\ =5 \sqrt{2^3} -3 \sqrt{2} + \sqrt{5} +5 \sqrt{2^5} -4 \sqrt{5}= \\ \\ =5*2 \sqrt{2} -3 \sqrt{2} + \sqrt{5} +5*2^2 \sqrt{2} -4 \sqrt{5} = \\ \\= 10 \sqrt{2} -3 \sqrt{2} + \sqrt{5} +20 \sqrt{2} -4 \sqrt{5} = \\ \\ =27 \sqrt{2} -3 \sqrt{5} = \\ \\ =3*(9 \sqrt{2}- \sqrt{5}) 5 \sqrt{8} -3 \sqrt{2} + \sqrt{5} +5 \sqrt{32} -4 \sqrt{5} = \\ \\ =5 \sqrt{2^3} -3 \sqrt{2} + \sqrt{5} +5 \sqrt{2^5} -4 \sqrt{5}= \\ \\ =5*2 \sqrt{2} -3 \sqrt{2} + \sqrt{5} +5*2^2 \sqrt{2} -4 \sqrt{5} = \\ \\= 10 \sqrt{2} -3 \sqrt{2} + \sqrt{5} +20 \sqrt{2} -4 \sqrt{5} = \\ \\ =27 \sqrt{2} -3 \sqrt{5} = \\ \\ =3*(9 \sqrt{2}- \sqrt{5})](https://tex.z-dn.net/?f=5+%5Csqrt%7B8%7D+-3+%5Csqrt%7B2%7D+%2B+%5Csqrt%7B5%7D+%2B5+%5Csqrt%7B32%7D+-4+%5Csqrt%7B5%7D+%3D+%5C%5C++%5C%5C+%3D5+%5Csqrt%7B2%5E3%7D+-3+%5Csqrt%7B2%7D+%2B++%5Csqrt%7B5%7D+%2B5+%5Csqrt%7B2%5E5%7D+-4+%5Csqrt%7B5%7D%3D+%5C%5C++%5C%5C+%3D5%2A2+%5Csqrt%7B2%7D+-3+%5Csqrt%7B2%7D+%2B+%5Csqrt%7B5%7D+%2B5%2A2%5E2+%5Csqrt%7B2%7D+-4+%5Csqrt%7B5%7D+%3D+%5C%5C++%5C%5C%3D+10+%5Csqrt%7B2%7D+-3+%5Csqrt%7B2%7D+%2B++%5Csqrt%7B5%7D+%2B20+%5Csqrt%7B2%7D+-4+%5Csqrt%7B5%7D+%3D+%5C%5C++%5C%5C+%3D27+%5Csqrt%7B2%7D+-3+%5Csqrt%7B5%7D+%3D+%5C%5C++%5C%5C+%3D3%2A%289+%5Csqrt%7B2%7D-+%5Csqrt%7B5%7D%29++)
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3)
![\sqrt{2x^2y^4}-3xy^2 \sqrt{2}+5 \sqrt{8x^2y^4}= \\ \\ =xy^2 \sqrt{2}-3xy^2 \sqrt{2}+5*2xy^2 \sqrt{2}= \\ \\ =8xy^2 \sqrt{2} \sqrt{2x^2y^4}-3xy^2 \sqrt{2}+5 \sqrt{8x^2y^4}= \\ \\ =xy^2 \sqrt{2}-3xy^2 \sqrt{2}+5*2xy^2 \sqrt{2}= \\ \\ =8xy^2 \sqrt{2}](https://tex.z-dn.net/?f=+%5Csqrt%7B2x%5E2y%5E4%7D-3xy%5E2+%5Csqrt%7B2%7D%2B5+%5Csqrt%7B8x%5E2y%5E4%7D%3D+%5C%5C++%5C%5C+%3Dxy%5E2+%5Csqrt%7B2%7D-3xy%5E2+%5Csqrt%7B2%7D%2B5%2A2xy%5E2+%5Csqrt%7B2%7D%3D+%5C%5C++%5C%5C+%3D8xy%5E2+%5Csqrt%7B2%7D++++++)
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4)
![\sqrt[3]{16} + \sqrt[3]{2} - \sqrt[3]{128} = \\ \\ =\sqrt[3]{2^4} + \sqrt[3]{2} - \sqrt[3]{2^7}= \\ \\ = \sqrt[3]{2^3*2^1} +\sqrt[3]{2} - \sqrt[3]{2^3*2^3*2} = \\ \\ =2 \sqrt[3]{2} +\sqrt[3]{2} - 4 \sqrt[3]{2} = \\ \\ =- \sqrt[3]{2} \sqrt[3]{16} + \sqrt[3]{2} - \sqrt[3]{128} = \\ \\ =\sqrt[3]{2^4} + \sqrt[3]{2} - \sqrt[3]{2^7}= \\ \\ = \sqrt[3]{2^3*2^1} +\sqrt[3]{2} - \sqrt[3]{2^3*2^3*2} = \\ \\ =2 \sqrt[3]{2} +\sqrt[3]{2} - 4 \sqrt[3]{2} = \\ \\ =- \sqrt[3]{2}](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B16%7D+%2B+%5Csqrt%5B3%5D%7B2%7D+-+%5Csqrt%5B3%5D%7B128%7D+%3D+%5C%5C++%5C%5C+%3D%5Csqrt%5B3%5D%7B2%5E4%7D+%2B+%5Csqrt%5B3%5D%7B2%7D+-+%5Csqrt%5B3%5D%7B2%5E7%7D%3D+%5C%5C++%5C%5C+%3D+%5Csqrt%5B3%5D%7B2%5E3%2A2%5E1%7D+%2B%5Csqrt%5B3%5D%7B2%7D+-++%5Csqrt%5B3%5D%7B2%5E3%2A2%5E3%2A2%7D+%3D+%5C%5C++%5C%5C+%3D2+%5Csqrt%5B3%5D%7B2%7D+%2B%5Csqrt%5B3%5D%7B2%7D+-+4+%5Csqrt%5B3%5D%7B2%7D+%3D+%5C%5C++%5C%5C+%3D-+%5Csqrt%5B3%5D%7B2%7D+)
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6)
![\sqrt{ \frac{72}{2} } = \frac{ \sqrt{72} }{ \sqrt{2} } = \frac{\sqrt{2^3*3^2} }{ \sqrt{2} } = \frac{2*3* \sqrt{2} }{ \sqrt{2} } =6 \sqrt{ \frac{72}{2} } = \frac{ \sqrt{72} }{ \sqrt{2} } = \frac{\sqrt{2^3*3^2} }{ \sqrt{2} } = \frac{2*3* \sqrt{2} }{ \sqrt{2} } =6](https://tex.z-dn.net/?f=+%5Csqrt%7B+%5Cfrac%7B72%7D%7B2%7D+%7D+%3D+%5Cfrac%7B+%5Csqrt%7B72%7D+%7D%7B+%5Csqrt%7B2%7D+%7D+%3D++%5Cfrac%7B%5Csqrt%7B2%5E3%2A3%5E2%7D+%7D%7B+%5Csqrt%7B2%7D+%7D+%3D+%5Cfrac%7B2%2A3%2A+%5Csqrt%7B2%7D+%7D%7B+%5Csqrt%7B2%7D+%7D+%3D6)
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Saludos.
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Saludos.
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