Question

Tính

a)\(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)

b)\(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)

c) \(\sqrt{17-12\sqrt{2}}-\sqrt{24-8\sqrt{8}}\)

d)\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)

Answer 1

Bài làm của: Phùng Khánh Linh

c)\(\sqrt{17-12\sqrt{2}}-\sqrt{24-8\sqrt{8}}\)

= \(\sqrt{3^2-2.3.2\sqrt{2}+\left(2\sqrt{2}\right)^2}\) \(-\) \(\sqrt{4^2-2.4.\sqrt{8}+\left(\sqrt{8}\right)^2}\)

= \(\sqrt{\left(3-2\sqrt{2}\right)^2}\) \(-\) \(\sqrt{\left(4-\sqrt{8}\right)^2}\)

= \(\left|3-2\sqrt{2}\right|-\left|4-\sqrt{8}\right|\)

= (3 - 2\(\sqrt{2}\)) - (4 - \(\sqrt{8}\))

= 3 - 2\(\sqrt{2}\) - 4 + \(\sqrt{8}\)

= -1

Answer 2

\(a.\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}=\sqrt{3+2\sqrt{3}.1+1}-\sqrt{3-2\sqrt{3}.1+1}=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-1\right)^2}=\text{|}\sqrt{3}+1\text{|}-\text{|}\sqrt{3}-1\text{|}=2\)\(b.\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}=\sqrt{5-4\sqrt{5}+4}-\sqrt{5+4\sqrt{5}+4}=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{\left(\sqrt{5}+2\right)^2}=\text{|}\sqrt{5}-2\text{|}-\text{|}\sqrt{5}+2\text{|}=-4\) Còn lại tương tự nhé .