\(\sqrt{8-2\sqrt{7}}-\sqrt{23-8\sqrt{7}}=\) \(\sqrt{1-2\sqrt{7}+7}-\sqrt{7-2.4.\sqrt{7}+16}\)

\(=\sqrt{\left(1-\sqrt{7}\right)^2}-\sqrt{\left(\sqrt{7}-4\right)^2}\)

\(=\sqrt{7}-1-\left(-\sqrt{7}+4\right)\)

\(=\sqrt{7}-1+\sqrt{7}-4\)\(=2\sqrt{7}-5\)

chúc bn học tốt

=\(\sqrt{\left(\sqrt{7}-1\right)^2}\)- \(\sqrt{\left(4-\sqrt{7}\right)^2}\)

= \(\sqrt{7}\)- 1 - 4 + \(\sqrt{7}\)

= \(2\sqrt{7}\)-5

đ/á ra hơi kì

#mã mã#

mình nghĩ là hai bn làm đúng đó

Trả lời:

\(D=\sqrt{11-6\sqrt{2}}-3+\sqrt{2}\)

\(D=\sqrt{9-6\sqrt{2}+2}-3+\sqrt{2}\)

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

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

\(D=0\)

\(E=\sqrt{23+8\sqrt{7}}-\sqrt{7}\)

\(E=\sqrt{16+8\sqrt{7}+7}-\sqrt{7}\)

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

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

\(E=4\)

\(\sqrt{8+3\sqrt{7}}-\sqrt{8-3\sqrt{7}}\)

\(=\frac{\sqrt{16+6\sqrt{7}}}{\sqrt{2}}-\frac{\sqrt{16-6\sqrt{7}}}{\sqrt{2}}\)

\(=\frac{\sqrt{\left(\sqrt{7}\right)^2+2.\sqrt{7}.3+3^2}}{\sqrt{2}}-\frac{\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}.3+3^2}}{\sqrt{2}}\)

\(=\frac{\sqrt{\left(\sqrt{7}+3\right)^2}}{\sqrt{2}}-\frac{\sqrt{\left(3-\sqrt{7}\right)^2}}{\sqrt{2}}\)

\(=\frac{\sqrt{7}+3}{\sqrt{2}}-\frac{3-\sqrt{7}}{\sqrt{2}}\)

\(=\frac{\sqrt{7}+3-3+\sqrt{7}}{\sqrt{2}}=\frac{2\sqrt{7}}{\sqrt{2}}=\sqrt{14}\)

Thanks bn♥

\(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\cdot\sqrt{7}+7\sqrt{8}\)

\(=\left(3\sqrt{7}-2\sqrt{14}\right)\cdot\sqrt{7}+14\sqrt{2}\)

\(=21-14\sqrt{2}+14\sqrt{2}\)

=21

\(=\left(3\sqrt{2}-2\sqrt{2}+\sqrt{14}\right).\sqrt{2}-\sqrt{7}\\ =\left(\sqrt{2}+\sqrt{14}\right).\sqrt{2}-\sqrt{7}\\ =2+2\sqrt{7}-\sqrt{7}\\ =2+\sqrt{7}\)

\(A=\dfrac{\sqrt{8}-\sqrt{7}}{8-7}+\sqrt{25\times7}-2\sqrt{2}\\ =\sqrt{8}-\sqrt{7}+5\sqrt{7}-2\sqrt{2}\\ =2\sqrt{2}-\sqrt{7}+5\sqrt{7}-2\sqrt{2}\\ =4\sqrt{7}\)

Bạn ghi lại đề dùm

\(\sqrt{8-2\sqrt{7}-\left[\left(\sqrt{7}+1\right)^2\right]}\)

\(\sqrt{8-2\sqrt{7}-\sqrt{7}-1}\)

\(\Leftrightarrow\sqrt{7-\sqrt{7}}\)

\(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)

= \(\sqrt{7}-1-\left(1+\sqrt{7}\right)\)

\(=\sqrt{7}-1-\sqrt{7}-1\)

= -2