Explicación paso a paso:
Resolución:
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1) [tex]5\sqrt{8} -\sqrt{32} +3\sqrt{18}[/tex]
Descomponemos las raíces en factores primos:
[tex]5\sqrt{2^2*2} -\sqrt{2^5} +3\sqrt{3^2*2}[/tex]
Operamos:
[tex]5\sqrt{2^2} *\sqrt{2} -\sqrt{2^{4}*2} +3\sqrt{3^2*2}[/tex]
[tex]5*2*\sqrt{2} -\sqrt{2^4} *\sqrt{2} +3*\sqrt{3^2} *\sqrt{2}[/tex]
[tex]10\sqrt{2} -2^2*\sqrt{2} +3*3*\sqrt{2}[/tex]
[tex]10\sqrt{2} -4\sqrt{2} +9\sqrt{2}[/tex]
[tex]6\sqrt{2} +9\sqrt{2}[/tex]
[tex]15\sqrt{2}[/tex]
Solución:
[tex]15\sqrt{2}[/tex]
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2) [tex]4\sqrt{2} -3\sqrt{48} +2\sqrt{27} +3\sqrt{75}[/tex]
Descomponemos la raíces en factores primos:
[tex]4\sqrt{2} -3\sqrt{2^4*3 } +2\sqrt{3^2*3} +3\sqrt{5^2*3}[/tex]
Operamos:
[tex]4\sqrt{2} -3*\sqrt{2^4} *\sqrt{3} +2*\sqrt{3^2} *\sqrt{3} +3*\sqrt{5^2} *\sqrt{3}[/tex]
[tex]4\sqrt{2} -3*2^2*\sqrt{3} +2*3*\sqrt{3} +3*5*\sqrt{3}[/tex]
[tex]4\sqrt{2} -3*4*\sqrt{3} +6\sqrt{3} +15\sqrt{3}[/tex]
[tex]4\sqrt{2} -12\sqrt{3} +6\sqrt{3} +15\sqrt{3}[/tex]
[tex]4\sqrt{2} -12\sqrt{3} +21\sqrt{3}[/tex]
[tex]4\sqrt{2} +9\sqrt{3}[/tex]
Solución:
[tex]4\sqrt{2} +9\sqrt{3}[/tex]
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3) [tex]\sqrt{27} -\sqrt{12} +\sqrt{75}[/tex]
Descomponemos las raíces en factores primos:
[tex]\sqrt{3^2*3} -\sqrt{2^2*3} +\sqrt{5^2*3}[/tex]
Operamos:
[tex]\sqrt{3^2} *\sqrt{3} -\sqrt{2^2} *\sqrt{3} +\sqrt{5^2} *\sqrt{3}[/tex]
[tex]3\sqrt{3} -2\sqrt{3} +5\sqrt{3}[/tex]
[tex]1\sqrt{3} +5\sqrt{3}[/tex]
[tex]6\sqrt{3}[/tex]
Solución:
[tex]6\sqrt{3}[/tex]
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4) [tex]7\sqrt[3]{81} +5\sqrt[3]{24} -2\sqrt[3]{375}[/tex]
Descomponemos las raíces en factores primos:
[tex]7\sqrt[3]{3^3*3}+5\sqrt[3]{2^3*3} -2\sqrt[3]{5^3*3}[/tex]
Operamos:
[tex]7*\sqrt[3]{3^3} *\sqrt[3]{3} +5*\sqrt[3]{2^3}*\sqrt[3]{3} -2*\sqrt[3]{5^3} *\sqrt[3]{3}[/tex]
[tex]7*3*\sqrt[3]{3} +5*2*\sqrt[3]{3} -2*5*\sqrt[3]{3}[/tex]
[tex]21\sqrt[3]{3} +10\sqrt[3]{3} -10\sqrt[3]{3}[/tex]
[tex]21\sqrt[3]{3}[/tex]
Solución:
[tex]21\sqrt[3]{3}[/tex]