\(\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)
\(\sqrt{17-\sqrt{33}}.\sqrt{17+\sqrt{33}}=\sqrt{\left(17-\sqrt{33}\right)\left(17+\sqrt{33}\right)}=\sqrt{17^2-33}=16\)
\(x^2+x+1=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0;\forall x\in R\) nên \(\sqrt{x^2+x+1}\) xác định với mọi x thuộc R
\(\sqrt{3+\sqrt{13+\sqrt{48}}}=\sqrt{3+\sqrt{\left(2\sqrt{3}+1\right)^2}}=\sqrt{3+2\sqrt{3}+1}=\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}+1\right)^2}=1+\sqrt{3}\)
\(x^2\ge0\Rightarrow16-x^2\le16\Rightarrow\sqrt{16-x^2}\le\sqrt{16}=4\)
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