Can $\frac{4+\sqrt{40}}{2}$ be simplified to $2+\sqrt{10}$ manually?
Simplify square root in fraction?
0
$\begingroup$
arithmetic
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0Too trivial to be discussed here. – 2014-06-19
2 Answers
11
$\frac{4+\sqrt{40}}{2} = \frac{4+\sqrt{4\times 10}}{2} =\frac{4+\sqrt{4}\times\sqrt{10}}{2} = \frac{4+2\sqrt{10}}{2} = 2+\sqrt{10}$
4
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
$\frac{4+\sqrt{40}}{2} = \frac{4}{2}+\frac{\sqrt{40}}{2} =2+\frac{\sqrt{40}}{\sqrt{4}}=2+\sqrt{\frac{40}{4}} = 2+\sqrt{10}.$