Question

Bài 1.3, 1.4

 

Answer 1

Bài 1.3:

a) Ta có: \(\left\{{}\begin{matrix}5\sqrt{7}=\sqrt{25.7}=\sqrt{175}\\7\sqrt{5}=\sqrt{49.5}=\sqrt{245}\end{matrix}\right.\)

Do \(245>175\Rightarrow7\sqrt{5}>5\sqrt{7}\Rightarrow\sqrt{7\sqrt{5}}=\sqrt{5\sqrt{7}}\)

b) Ta có: \(21+4\sqrt{5}=\left(2\sqrt{5}\right)^2+2.2\sqrt{5}+1=\left(2\sqrt{5}+1\right)^2\)

\(\Rightarrow7-\sqrt{21+4\sqrt{5}}=7-\left(2\sqrt{5}+1\right)=6-2\sqrt{5}\)

Lại có: \(\left(\sqrt{5}-1\right)^2=6-2\sqrt{5}\)

\(\Rightarrow7-\sqrt{21+4\sqrt{5}}=\left(\sqrt{5}-1\right)^2\) \(\Rightarrow\sqrt{7-\sqrt{21+4\sqrt{5}}}=\sqrt{5}-1\)