tính √(3- √5)+ √(3+ √5)

Đáp án:

Giải thích các bước giải:

$\sqrt{(3-\sqrt{5})}$ + $\sqrt{(3+\sqrt{5})}$ = $\sqrt{\dfrac{6-2\sqrt{5}}{2}}$ + $\sqrt{\dfrac{6+2\sqrt{5}}{2}}$ = $\dfrac{\sqrt{5} -1 + \sqrt{5}+1}{2}$ = $\dfrac{2\sqrt{5}}{2}$ = $\sqrt[]{5}$ 

`\sqrt{(3-\sqrt{5})}+\sqrt{(3+\sqrt{5})}`

`=(\sqrt{2}\sqrt{(3-\sqrt{5})})/(\sqrt{2})+(\sqrt{2}\sqrt{(3+\sqrt{5})})/(\sqrt{2})`

`=(\sqrt{2(3-\sqrt{5})})/(\sqrt{2])+(\sqrt{2(3+\sqrt{5})})/(\sqrt{2})`

`=(\sqrt{6-2\sqrt{5}})/(\sqrt{2})+(\sqrt{6+2\sqrt{5}})/(\sqrt{2})`

`=(\sqrt{5-2\sqrt{5}+1})/(\sqrt{2})+(\sqrt{5+2\sqrt{5}+1})/(\sqrt{2})`

`=(\sqrt{(\sqrt{5}-1)^2})/(\sqrt{2})+(\sqrt{(\sqrt{5}+1)^2})/(\sqrt{2})`

`=(|\sqrt{5}-1|)/(\sqrt{2})+(|\sqrt{5}+1|)/(\sqrt{2})`

`=(\sqrt{5}-1)/(\sqrt{2})+(\sqrt{5}+1)/(\sqrt{2})`

`=(\sqrt{5}-1+\sqrt{5}+1)/(\sqrt{2})`

`=(2\sqrt{5})/(\sqrt{2})`

`=(2\sqrt{5}\sqrt{2})/(\sqrt{2}\sqrt{2})`

`=(2\sqrt{10})/(2)`

`=\sqrt{10}`