Respuesta:
[tex]\sqrt{1278}=3\sqrt{142}\quad \left(\mathrm{Decimal:\quad }\:35.74912)[/tex]
Explicación paso a paso:
[tex]\sqrt{1278}\\desconpocicion/en/factores/primos/de1278=2\cdot \:3^2\cdot \:71\\=\sqrt{2\cdot \:3^2\cdot \:71}\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \sqrt{ab}=\sqrt{a}\sqrt{b},\:\quad \:a\ge 0,\:b\ge 0\\\sqrt{2\cdot \:3^2\cdot \:71}=\sqrt{3^2}\sqrt{2\cdot \:71}\\=\sqrt{3^2}\sqrt{2\cdot \:71}\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \sqrt{a^2}=a,\:\quad \:a\ge 0\\\sqrt{3^2}=3\\=3\sqrt{2\cdot \:71}\\\mathrm{Multiplicar\:los\:numeros:}\:2\cdot \:71=142\\=3\sqrt{142}[/tex]
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Verified answer
Respuesta:
[tex]\sqrt{1278}=3\sqrt{142}\quad \left(\mathrm{Decimal:\quad }\:35.74912)[/tex]
Explicación paso a paso:
[tex]\sqrt{1278}\\desconpocicion/en/factores/primos/de1278=2\cdot \:3^2\cdot \:71\\=\sqrt{2\cdot \:3^2\cdot \:71}\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \sqrt{ab}=\sqrt{a}\sqrt{b},\:\quad \:a\ge 0,\:b\ge 0\\\sqrt{2\cdot \:3^2\cdot \:71}=\sqrt{3^2}\sqrt{2\cdot \:71}\\=\sqrt{3^2}\sqrt{2\cdot \:71}\\\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \sqrt{a^2}=a,\:\quad \:a\ge 0\\\sqrt{3^2}=3\\=3\sqrt{2\cdot \:71}\\\mathrm{Multiplicar\:los\:numeros:}\:2\cdot \:71=142\\=3\sqrt{142}[/tex]
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