Question

Thực hiện khai căn sau

a \(\sqrt{5-2\sqrt{6}}\)

 

b\(\sqrt{3-2\sqrt{2}}\)

c \(\sqrt{21+4\sqrt{5}}\)

d \(\sqrt{11+4\sqrt{7}}\)

 

Answer 1

a) \(\sqrt{5-2\sqrt{6}}=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}=\sqrt{3}-\sqrt{2}\)

b) \(\sqrt{3-2\sqrt{2}}=\sqrt{\left(\sqrt{2}-1\right)^2}=\sqrt{2}-1\)

c) \(\sqrt{21+4\sqrt{5}}=\sqrt{\left(2\sqrt{5}+1\right)^2}=2\sqrt{5}+1\)

d) \(\sqrt{11+4\sqrt{7}}=\sqrt{\left(\sqrt{7}+2\right)^2}=\sqrt{7}+2\)

Answer 2

a

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

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

b,

\(\sqrt{3-2\sqrt{2}}=\sqrt{\sqrt{2}^2-2.\sqrt{2}.1+1^2}\)

\(=\sqrt{\left(\sqrt{2}-1\right)^2}=\sqrt{2}-1\)

c,\(\sqrt{11+4\sqrt{7}}=\sqrt{11+2\sqrt{28}}=\sqrt{\sqrt{7}^2+2.\sqrt{7}.\sqrt{4}+\sqrt{4}^2}\)

\(=\sqrt{\left(\sqrt{7}+\sqrt{4}\right)^2}=\sqrt{7}+\sqrt{4}\)

Answer 3

a) \(\sqrt{5-2\sqrt{6}}=25\sqrt{-2\sqrt{6}}\)

b) \(\sqrt{3-2\sqrt{2}}=9\sqrt{-2\sqrt{2}}\)

c) \(\sqrt{11+4\sqrt{7}}=121\sqrt{4\sqrt{7}}\)

Answer 4

c) \(\sqrt{21+4\sqrt{5}}=\sqrt{21+2.2\sqrt{5}}=\sqrt{20+1+2.\sqrt{20}}=\sqrt{\left(\sqrt{20}+1\right)^2}=2\sqrt{5}+1\)

Answer 5

a) \(\sqrt{5-2\sqrt{6}}=\sqrt{\sqrt{2}^2-2.\sqrt{2}.\sqrt{3}+\sqrt{3}^2}\)

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

b) \(\sqrt{3-2\sqrt{2}}=\sqrt{\sqrt{2}^2-2.\sqrt{2}.1+1^2}\)

\(=\sqrt{\left(\sqrt{2}-1\right)^2}=\sqrt{2}-1\)

c) \(\sqrt{11+4\sqrt{7}}=\sqrt{11+2\sqrt{28}}=\sqrt{\sqrt{7}^2+2.\sqrt{7}.\sqrt{4}+\sqrt{4}^2}\)

\(=\sqrt{\left(\sqrt{7}+\sqrt{4}\right)^2}=\sqrt{7}+\sqrt{4}\)