\(\sqrt{13+30\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)
\(=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}\right)^2}+4\sqrt{2}+1^2}}\)
\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1^2}}\)
\(=\sqrt{13+30\sqrt{\left(\sqrt{2}\right)^2+2\sqrt{2}+1^2}}\)
\(=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)
\(=\sqrt{5^2+2.5.3\sqrt{2}+\left(3+\sqrt{2}\right)^2}\)
\(=\sqrt{\left(5+3+\sqrt{2}\right)^2}\)
\(=\sqrt{\left(5+6\right)}=\sqrt{11}\)
\(=5+6=11\)
a)=1
b)=\(3\sqrt{2}+5\)
a) \(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{29-12\sqrt{5}}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{(2\sqrt{5}+3)^2}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-(2\sqrt{5}+3)}}\)
=\(\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)
=\(\sqrt{\sqrt{5}-(\sqrt{5}-1)}\)
=\(\sqrt{1}=1\)
b) \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
=\(\sqrt{13+30\sqrt{2+\sqrt{(2\sqrt{2}+1)^2}}}\)
=\(\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)
=\(\sqrt{13+30\sqrt{(2+1)^2}}\)
=\(\sqrt{13+30.(2+1)}\)
=\(\sqrt{43+30\sqrt{2}}=\sqrt{(3\sqrt{2}+5)^2}\)
=\(3\sqrt{2}+5\)
a) =1
b) = \(3\sqrt{2}+5\)
a) = 1
b) =\(3\sqrt{2}+5\)
\(a,\sqrt{\sqrt{5}-\sqrt{9-\sqrt{29-12\sqrt{5}}}}\\ =\sqrt{\sqrt{5}-\sqrt{\left(2\sqrt{5}+3\right)^2}}\\ =\sqrt{\sqrt{5}-\sqrt{9-\left(2\sqrt{5}+3\right)}}\\ =\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\\ =\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\\ =\sqrt{5-\sqrt{\left(\sqrt{5}-1\right)}}\\ =\sqrt{1}\\ =1\)
\(b,\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\\ =\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}\\ =\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\\ =\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\\ =\sqrt{13+30\left(\sqrt{2}+1\right)}\\ =\sqrt{43+30\sqrt{2}}\\ =\sqrt{\left(3\sqrt{2}+5\right)^2}\\ =3\sqrt{2}+5\)
a\()\)\(\sqrt{\sqrt{5-\sqrt{9-\sqrt{29-12\sqrt{5}}}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{2\sqrt{5+3)^2}}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-(2\sqrt{5}+3)^{ }}}\)
=\(\sqrt{\sqrt{5}}-\sqrt{9-(2\sqrt{5+3)}}\)
=\(\sqrt{\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
=\(\sqrt{\sqrt{5}}-\sqrt{(\sqrt{5-1)^2}}\)
=\(\sqrt{\sqrt{5}}-(\sqrt{5-1)}\)
=\(\sqrt{1}=1\)
b\()\)\(\sqrt{13+30\sqrt{2+2\sqrt{2+1}}}\)
=\(\sqrt{13+30\sqrt{2+\sqrt{(2\sqrt{2+1)^2}}}}\)
=\(\sqrt{13+30\sqrt{2+2\sqrt{2+1}}}\)
=\(\sqrt{13+30.(\sqrt{2}+1)}\)
=\(\sqrt{43+30\sqrt{2}}\)
=\(\sqrt{(3\sqrt{2}+5)^2}=3\sqrt{2+5}\)
a) = 1 b) =\(3\sqrt{2}+5\)
a) = 1
b) =\(3\sqrt{2}+5\)
a, \(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{29-12\sqrt{5}}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{\left(2\sqrt{5}+3\right)^2}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-\left(2\sqrt{5}+3\right)}}\)
=\(\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)
=\(\sqrt{\sqrt{5}-\left(\sqrt{5}-1\right)}\)
=\(\sqrt{1}\)=\(1\)
b, \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
=\(\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}\)
=\(\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)
=\(\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)
=\(\sqrt{13+30\left(\sqrt{2}+1\right)}\)
=\(\sqrt{43+30\sqrt{2}}\)
=\(\sqrt{\left(3\sqrt{2}+5\right)^2}\)
=\(3\sqrt{2}+5\)
a, 1
b,\(3\sqrt{2+5}\)
a) 1
b) 3\(\sqrt{2}\)+ 5
a) \(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{29-12\sqrt{5}}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{\left(2\sqrt{5}+3\right)^2}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-2\sqrt{5}-3}}\)
=\(\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)
=\(\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)
=\(\sqrt{\sqrt{5}-\sqrt{5}+1}\)
=\(\sqrt{1}\)=1
b)\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
=\(\sqrt{13+30\sqrt{2+\sqrt{8+4\sqrt{2}+1}}}\)
=\(\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)
=\(\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)
=\(\sqrt{13+30\left(\sqrt{2}+1\right)}\)
=\(\sqrt{13+30\sqrt{2}+30}\)
=\(\sqrt{\left(3\sqrt{2}+5\right)^2}\)
=\(3\sqrt{2}+5\)
a) = 1
b) = 3\(\sqrt{2}+5\)
a)1
b)\(3\sqrt{2}+5\)
a) 1
b) 3\(\sqrt{2}\)+5
a) 1
b) \(3\sqrt{2}\)+ 5
a) 1
b) \(3\sqrt{2}\)+ 5
a) 1
b) \(3\sqrt{2}+5\)
a) 1
b) 3\(\sqrt{2}\) +5
a) 1
b) 3\(\sqrt{2}\)+ 5
a) -1
b) 3\(\sqrt{2}\)+ 5
a) 1
b) 3\(\sqrt{2}\)+ 5
a) 1
b)5+ 3\(\sqrt{2}\)
a)\(\sqrt{\sqrt{5}-\sqrt{12-2\sqrt{5}}}\)
b)\(3\sqrt{2}+5\)
a) 1
b) \(3\sqrt{2}+5\)
a)\(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{29-12\sqrt{5}}}}\)= \(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{\left(2\sqrt{5}-3\right)^2}}}\)=\(\sqrt{\sqrt{5}-\sqrt{9-\left(2\sqrt{5}-3\right)}}\)
=\(\sqrt{\sqrt{5}-\sqrt{9-2\sqrt{5}+3}}\)=\(\sqrt{\sqrt{5}-\sqrt{12-2\sqrt{5}}}\)=( sai đề)
b)\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)= \(\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)}}}\)=\(\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)
=\(\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)=\(\sqrt{13+30\left(\sqrt{2}+1\right)}\)=\(\sqrt{13+30\sqrt{2}+30}\)=\(\sqrt{\left(3\sqrt{2}+5\right)^2}\)
=\(3\sqrt{2}+5\)
a.\(=\sqrt{\sqrt{5}-\sqrt{9}-\sqrt{\left(2\sqrt{5}+3\right)^2}}=\sqrt{\sqrt{5}-\sqrt{9-\left(2\sqrt{5}+3\right)}}=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}=\sqrt{\sqrt{5-\left(\sqrt{5}-1\right)}}}=\sqrt{\sqrt{5}-\left|\sqrt{5}-1\right|}=\sqrt{\sqrt{5-\left(\sqrt{5}-1\right)}}=\sqrt{1}=1\)b.\(=\sqrt{13+30\sqrt{2+\left(2\sqrt{2}+1\right)^2}}=\sqrt{13+30\sqrt{2}+2\sqrt{2}+1}=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{13+30\sqrt{2+30}}=\sqrt{43+30\sqrt{2}}=\sqrt{\left(3\sqrt{2}+5\right)^2}=3\sqrt{2}+5\)
a) \(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{29-12\sqrt{5}}}}\)\(=\sqrt{\sqrt{5}-\sqrt{9-\sqrt{\left(2\sqrt{5}-3\right)^2}}}\)
\(=\sqrt{\sqrt{5}-\sqrt{9-\left(2\sqrt{5}-3\right)}}=\sqrt{\sqrt{5}-\sqrt{9-2\sqrt{5}+3}}\)
\(=\sqrt{\sqrt{5}-\sqrt{12-2\sqrt{5}}}\)(sai đề)
b) \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)}}}=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}=\sqrt{13+30\left(\sqrt{2}+1\right)}\)
\(=\sqrt{13+30\sqrt{2}+30}=\sqrt{\left(3\sqrt{2}+5\right)^2}=3\sqrt{2}+5\)