0
$\begingroup$

Can $\frac{4+\sqrt{40}}{2}$ be simplified to $2+\sqrt{10}$ manually?

  • 7
    $\sqrt{40}=2\sqrt{10}$...2011-07-23
  • 0
    For more information,here: http://en.wikipedia.org/wiki/Nth_root2011-07-24
  • 0
    Too trivial to be discussed here.2014-06-19

2 Answers 2

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

  1. $\dfrac{A+B}{C}=\dfrac{A}{C}+\dfrac{B}{C}$,
  2. $2=\sqrt{4}$,
  3. and $\dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b} }$.

Then

$$\frac{4+\sqrt{40}}{2} = \frac{4}{2}+\frac{\sqrt{40}}{2} =2+\frac{\sqrt{40}}{\sqrt{4}}=2+\sqrt{\frac{40}{4}} = 2+\sqrt{10}.$$