Question

\(\sqrt{\left(\sqrt{7}-5\right)^2}+\sqrt{\left(2-\sqrt{7}\right)^2}\)

\(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

\(\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)

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

Answer 1

Lời giải:

a. \(=|\sqrt{7}-5|+|2-\sqrt{7}|=5-\sqrt{7}+(\sqrt{7}-2)=3\)

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

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

c.

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

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

d.

$=\sqrt{(\sqrt{5}+1)^2}-\sqrt{(\sqrt{5}-1)^2}$

$=|\sqrt{5}+1|-|\sqrt{5}-1|=\sqrt{5}+1-(\sqrt{5}-1)=2$