Can $\frac{4+\sqrt{40}}{2}$ be simplified to $2+\sqrt{10}$ manually?
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7$\sqrt{40}=2\sqrt{10}$... – J. M. ain't a mathematician Jul 23 '11 at 12:30
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For more information,here: http://en.wikipedia.org/wiki/Nth_root – Jul 24 '11 at 01:42
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Too trivial to be discussed here. – Debashish Jun 19 '14 at 09:25
2 Answers
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$$\frac{4+\sqrt{40}}{2} = \frac{4+\sqrt{4\times 10}}{2} =\frac{4+\sqrt{4}\times\sqrt{10}}{2} = \frac{4+2\sqrt{10}}{2} = 2+\sqrt{10}$$
Asaf Karagila
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Observe that
- $\dfrac{A+B}{C}=\dfrac{A}{C}+\dfrac{B}{C}$,
- $2=\sqrt{4}$,
- and $\dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b} }$.
Then
$$\frac{4+\sqrt{40}}{2} = \frac{4}{2}+\frac{\sqrt{40}}{2} =2+\frac{\sqrt{40}}{\sqrt{4}}=2+\sqrt{\frac{40}{4}} = 2+\sqrt{10}.$$
Américo Tavares
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