Đáp án:
`a)\sqrt{31^2}`
`=|31|`
`=31`
`b)\sqrt{(2-2\sqrt{5})^2}-2\sqrt{5}`
`=|2-2\sqrt{5}|-2\sqrt{5}`
`=2\sqrt{5}-2-2\sqrt{5}`
`=-2`
`c)C=\sqrt{4a^2}+2a`
`=|2a|+2a`
Nếu `a>=0=>|2a|=2a`
`=>C=2a+2a=4a`
Nếu `a<=0=>|2a|=-2a`
`=>C=-2a+2a=0`
`d)\sqrt{(a-3)^2}(a>3)`
`=|a-3|`
`=a-3(do\,a>3=>a-3>0)`
`e)\sqrt{4+2\sqrt{3}}+\sqrt{3}`
`=\sqrt{3+2.\sqrt{3}+1}+\sqrt{3}`
`=\sqrt{(\sqrt{3}+1)^2}+\sqrt{3}`
`=\sqrt{3}+1+\sqrt{3}=2\sqrt{3}+1`.