\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)

\(=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{43+30\sqrt{2}}\)

\(=\sqrt{43+2\cdot\sqrt{450}}\)

\(=\sqrt{25+2\cdot5\cdot3\sqrt{2}+18}\)

\(=\sqrt{\left(5+3\sqrt{2}\right)^2}=5+3\sqrt{2}\)

Lời giải:

a. \(\sqrt{6-2\sqrt{5}}=\sqrt{5-2\sqrt{5}.\sqrt{1}+1}=\sqrt{(\sqrt{5}-1)^2}=\sqrt{5}-1\)

b. \(\sqrt{7-4\sqrt{3}}=\sqrt{4-2\sqrt{4}.\sqrt{3}+3}=\sqrt{(\sqrt{4}-\sqrt{3})^2}=\sqrt{4}-\sqrt{3}=2-\sqrt{3}\)

c.

\(\sqrt{3-2\sqrt{2}}-\sqrt{6-4\sqrt{2}}=\sqrt{2-2\sqrt{2}+1}-\sqrt{4-4\sqrt{2}+2}\)

\(=\sqrt{(\sqrt{2}-1)^2}-\sqrt{(\sqrt{4}-\sqrt{2})^2}\)

\(=|\sqrt{2}-1|-|\sqrt{4}-\sqrt{2}|=\sqrt{2}-1-(2-\sqrt{2})=2\sqrt{2}-3\)

d.

\(=\sqrt{13+30\sqrt{2+\sqrt{(\sqrt{8}+1)^2}}}=\sqrt{13+30\sqrt{2+\sqrt{8}+1}}\)

\(=\sqrt{13+30\sqrt{3+2\sqrt{2}}}=\sqrt{13+30\sqrt{(\sqrt{2}+1)^2}}\)

\(=\sqrt{13+30(\sqrt{2}+1)}=\sqrt{43+30\sqrt{2}}=\sqrt{18+2\sqrt{18.25}+25}\)

\(=\sqrt{(\sqrt{18}+\sqrt{25})^2}=\sqrt{18}+\sqrt{25}=5+3\sqrt{2}\)

a) \(\sqrt{6-2\sqrt{5}}=\sqrt{5}-1\)

b) \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)

c) \(\sqrt{3-2\sqrt{2}}-\sqrt{6-4\sqrt{2}}=\sqrt{2}-1-2+\sqrt{2}=-3+2\sqrt{2}\)

d) Ta có: \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

\(=\sqrt{13+30\sqrt{2+1+2\sqrt{2}}}\)

\(=\sqrt{13+30\left(\sqrt{2}+1\right)}\)

\(=\sqrt{43+30\sqrt{2}}\)

\(=5+3\sqrt{2}\)

a) Ta có: \(\sqrt{2}\left(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\right)\)

\(=\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}\)

\(=\sqrt{5}-1-\sqrt{5}-1=-2\)

b) Ta có: \(\sqrt{13+30\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)

\(=\sqrt{13+30\sqrt{2}+2\sqrt{2}+1}\)

\(=\sqrt{14+32\sqrt{2}}\)

c) Ta có: \(\sqrt{6+2\sqrt{5}-\sqrt{13+\sqrt{48}}}\)

\(=\sqrt{6+2\sqrt{5}-2\sqrt{3}-1}\)

\(=\sqrt{5+2\sqrt{5}-2\sqrt{3}}\)

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}=\sqrt{13+30\sqrt{2+\sqrt{1+4\sqrt{2}+8}}}=\sqrt{13+30\sqrt{2+\sqrt{1+2.2\sqrt{2}+\left(2\sqrt{2}\right)^2}}}=\sqrt{13+30\sqrt{2+\sqrt{\left(1+2\sqrt{2}\right)^2}}}=\sqrt{13+30\sqrt{3+2\sqrt{2}}}=\sqrt{13+30\sqrt{\left(1+\sqrt{2}\right)^2}}=\sqrt{13+30\left(1+\sqrt{2}\right)}=\sqrt{43+30\sqrt{2}}=\sqrt{\left(5+3\sqrt{2}\right)^2}=5+3\sqrt{2}\)

\(B=3\sqrt{2}-\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}\)

\(B=3\sqrt{2}-\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)

\(B=3\sqrt{2}-\sqrt{13+30\sqrt{3+2\sqrt{2}}}\)

\(B=3\sqrt{2}-\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)

\(B=3\sqrt{2}-\sqrt{13+30\left(\sqrt{2+1}\right)}\)

\(B=3\sqrt{2}-\sqrt{13+30\sqrt{2}+30}\)

\(B=3\sqrt{2}-\sqrt{43+30\sqrt{2}}\)

\(B=3\sqrt{2}-\sqrt{\left(3\sqrt{2}+5\right)^2}\)

\(B=3\sqrt{2}-3\sqrt{2}-5\)

\(B=-5\)

vậy \(B=-5\)

\(B=3\sqrt{2}-\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\\ \)

\(=3\sqrt{2}-\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}+1^2}}}\)

\(=3\sqrt{2}-\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)

\(=3\sqrt{2}-\sqrt{13+30\sqrt{\left(\sqrt{2}\right)^2+2\sqrt{2}+1}}\)

\(=3\sqrt{2}-\sqrt{13+30\left(\sqrt{2}+1\right)}\)

\(=3\sqrt{2}-\sqrt{13+30\sqrt{2}+30}\)

\(=3\sqrt{2}-\sqrt{43+30\sqrt{2}}\)

\(=3\sqrt{2}-\sqrt{\left(3\sqrt{2}\right)^2+2.5.3\sqrt{2}+5^2}\)

\(=3\sqrt{2}-3\sqrt{2}+5=5\)

rất chi tiết đó bạn

Jason làm sai rồi 

Despacito  làm mới đúng 

a,\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

\(=\sqrt{13+30\sqrt{3+2\sqrt{2}}}\\ =\sqrt{13+30\left(\sqrt{2}+1\right)}\)

\(=\sqrt{43+30\sqrt{2}}=5+3\sqrt{2}\)

b, \(\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)

\(\Leftrightarrow\sqrt{5-\sqrt{\left(2\sqrt{3}\right)^2+2.2\sqrt{3}+1}}+\sqrt{3+\sqrt{\left(2\sqrt{3}\right)^2+2.2\sqrt{3}+1}}\)

\(\Leftrightarrow\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}+\sqrt{3+\sqrt{\left(2\sqrt{3}+1\right)^2}}\)

\(\Leftrightarrow\sqrt{5-2\sqrt{3}-1}+\sqrt{3+2\sqrt{3}+1}\)

\(\Leftrightarrow\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(\Leftrightarrow\sqrt{3}-1+\sqrt{3}+1\)

\(\Leftrightarrow2\sqrt{3}\)

d,\(\left(\sqrt{3}-\sqrt{2}\right)\sqrt{5+2\sqrt{6}}\)

\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)\sqrt{3+2.\sqrt{2}\sqrt{3}+2}\)

\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)

\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)\)

\(\Leftrightarrow3-2\Leftrightarrow1\)

\(=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}\)

\(=\sqrt{13+30\sqrt{3+2\sqrt{2}}}\)

\(=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)

\(=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{43+30\sqrt{2}}\)

\(=\sqrt{\left(5+3\sqrt{2}\right)}=5+3\sqrt{2}\)