Question

rút gon căn thức

\(\sqrt{\dfrac{9}{4}-\sqrt{2}}\)

\(\sqrt{\dfrac{129}{16}+\sqrt{2}}\)

\(\sqrt{\dfrac{59}{25}+\dfrac{6}{5}\sqrt{2}}\)

Answer 1

_ \(\sqrt{\dfrac{9}{4}-\sqrt{2}}=\sqrt{\left(\sqrt{2}-\sqrt{\dfrac{1}{4}}\right)^2}=\left|\sqrt{2}-\dfrac{1}{2}\right|=-\dfrac{1}{2}+\sqrt{2}=\dfrac{-1+2\sqrt{2}}{2}\)

_ \(\sqrt{\dfrac{129}{16}+\sqrt{2}}\sqrt{\left(\sqrt{8}+\sqrt{\dfrac{1}{16}}\right)^2}=\left|2\sqrt{2}+\dfrac{1}{4}\right|=2\sqrt{2}+\dfrac{1}{4}=\dfrac{1+8\sqrt{2}}{4}\)

_ \(\sqrt{\dfrac{59}{25}+\dfrac{6}{5}\sqrt{2}}=\sqrt{\left(\sqrt{2}+\sqrt{\dfrac{9}{25}}\right)^2}=\left|\sqrt{2}+\dfrac{3}{5}\right|=\sqrt{2}+\dfrac{3}{5}=\dfrac{3+5\sqrt{2}}{5}\)

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