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\(A=\frac{2017-2016+2017\sqrt{2016}-2016\sqrt{2017}}{\sqrt{2016}+\sqrt{2017}+\sqrt{2016.2017}}\)
= \(\frac{\left(\sqrt{2017}-\sqrt{2016}\right)\left(\sqrt{2017}+\sqrt{2016}\right)+\sqrt{2016.2017}\left(\sqrt{2017}-\sqrt{2016}\right)}{\sqrt{2016}+\sqrt{2017}+\sqrt{2016.2017}}\)
= \(\frac{\left(\sqrt{2017}-\sqrt{2016}\right)\left(\sqrt{2016}+\sqrt{2017}+\sqrt{2016.2017}\right)}{\sqrt{2016}+\sqrt{2017}+\sqrt{2016.2017}}\)
= \(\sqrt{2017}-\sqrt{2016}\)
a)\(\sqrt{\left(4+\sqrt{2}\right)^2}=\left|4+\sqrt{2}\right|=4+\sqrt{2}\)
b)\(\sqrt{\left(3-\sqrt{3}\right)^2}=\left|3-\sqrt{3}\right|=3-\sqrt{3}\)
c)\(\sqrt{\left(4-\sqrt{17}\right)^2}=\left|4-\sqrt{17}\right|=\sqrt{17}-4\)
d)\(2\sqrt{3}+\sqrt{\left(2-\sqrt{3}\right)^2}=2\sqrt{3}+\left|2-\sqrt{3}\right|=2\sqrt{3}+2-\sqrt{3}\)
a) \(\sqrt{\left(5-\sqrt{3}\right)^2}=\left|5-\sqrt{3}\right|=5-\sqrt{3}\)
b) \(\sqrt{\left(1-\sqrt{2}\right)^2}=\left|1-\sqrt{2}\right|=-\left(1-\sqrt{2}\right)=\sqrt{2}-1\)( vì 1 < √2 )
c) \(\sqrt{\left(\sqrt{3}-2\right)^2}=\left|\sqrt{3}-2\right|=-\left(\sqrt{3}-2\right)=2-\sqrt{3}\)( vì √3 < 2 )
Lời giải:
a) $\sqrt{89^2}=|89|=89$
b) $\sqrt{2017}+\sqrt{(\sqrt{2017}-2016)^2}=\sqrt{2017}+|\sqrt{2017}-2016|$
$=\sqrt{2017}+2016-\sqrt{2017}=2016$