Question

B=\(\sqrt{4+\sqrt{7}}+\sqrt{4-\sqrt{7}}\)

tính dùm e nha

 

Answer 1

=3.741657387

Answer 2

\(B=\sqrt{4+\sqrt{7}}+\sqrt{4-\sqrt{7}}\)

\(\Rightarrow B=\dfrac{\sqrt{2}\left(\sqrt{4+\sqrt{7}}+\sqrt{4-\sqrt{7}}\right)}{\sqrt{2}}\)

\(\Rightarrow B=\dfrac{\sqrt{2}.\sqrt{4+\sqrt{7}}+\sqrt{2}.\sqrt{4-\sqrt{7}}}{\sqrt{2}}\)

\(\Rightarrow B=\dfrac{\sqrt{8+2\sqrt{7}}+\sqrt{8-2\sqrt{7}}}{\sqrt{2}}\)

\(\Rightarrow B=\dfrac{\sqrt{7+2\sqrt{7}+1}+\sqrt{7-2\sqrt{7}+1}}{\sqrt{2}}\)

\(\Rightarrow B=\dfrac{\sqrt{\left(\sqrt{7}+1\right)^2}+\sqrt{\left(\sqrt{7}-1\right)^2}}{\sqrt{2}}\)

\(\Rightarrow B=\dfrac{\sqrt{7}+1+\sqrt{7}-1}{\sqrt{2}}\)

\(\Rightarrow B=\dfrac{2\sqrt{7}}{\sqrt{2}}\)

\(\Rightarrow B=\sqrt{2}.\sqrt{7}\)

\(\Rightarrow B=\sqrt{14}\)