\(a,\sqrt{A}=\sqrt{13-2\sqrt{42}}\\ =\sqrt{13-2.\sqrt{6}.\sqrt{7}}\\ =\sqrt{7-2\sqrt{6}.\sqrt{7}+6}\\ =\sqrt{\left(\sqrt{7}-\sqrt{6}\right)^2}=\left|\sqrt{7}-\sqrt{6}\right|=\sqrt{7}-\sqrt{6}\\ b,\sqrt{A}=\sqrt{46-6\sqrt{5}}=\sqrt{46-2.3\sqrt{5}.1}\\ =\sqrt{45-2.3\sqrt{5}.1+1}\\ =\sqrt{\left(3\sqrt{5}-1\right)^2}\\ =\left|3\sqrt{5}-1\right|\\ =3\sqrt{5}-1\)
`A=13-2\sqrt{42}=7-2.\sqrt{7}.\sqrt{6}+6`
`=(\sqrt{7}-\sqrt{6})^{2}`
`=>\sqrt{A}=\sqrt{(\sqrt{7}-\sqrt{6})^{2}}=|\sqrt{7}-\sqrt{6}|=\sqrt{7}-\sqrt{6}`
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`A=46-6\sqrt{5}=46-2.\sqrt{9}.\sqrt{5}`
`=45-2.\sqrt{45}.1+1`
`=(\sqrt{45}-1)^{2}`
`=>\sqrt{A}=\sqrt{(\sqrt{45}-1)^{2}}=|\sqrt{45}-1|=3\sqrt{5}-1`
\(A=13-2\sqrt{42}=6-2\sqrt{6}\cdot\sqrt{7}+7=\left(\sqrt{6}-\sqrt{7}\right)^2\)
\(\Rightarrow\sqrt{A}=\sqrt{\left(\sqrt{6}-\sqrt{7}\right)^2}=\sqrt{7}-\sqrt{6}\)
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\(A=46-6\sqrt{5}=45+2\cdot3\sqrt{5}+1=\left(3\sqrt{5}+1\right)^2\)
\(\Rightarrow\sqrt{A}=\sqrt{\left(3\sqrt{5}+1\right)^2}=3\sqrt{5}+1\)
