Question

Rút gọn biểu thức chứa căn sau đến đơn giản nhất

a) \(\sqrt{11-2\sqrt{10}}\)

b)\(\sqrt{27-10\sqrt{2}}\)

c) \(\sqrt{4+2\sqrt{3}}\)

d) \(\sqrt{9+4\sqrt{5}}\)

e) \(\sqrt{21+4\sqrt{5}}\)

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Answer 1

a, \(\sqrt{11-2\sqrt{10}}=\sqrt{\left(\sqrt{10}\right)^2-2\sqrt{10}+1}=\sqrt{\left(\sqrt{10}+1\right)^2}\)

\(=\left|\sqrt{10}+1\right|=\sqrt{10}+1\)

b, \(\sqrt{27-10\sqrt{2}}=\sqrt{5^2-10\sqrt{2}+\left(\sqrt{2}\right)^2}=\sqrt{\left(5-\sqrt{2}\right)^2}\)

\(=\left|5-\sqrt{2}\right|=5-\sqrt{2}\)

c, \(\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}\right)^2+2\sqrt{3}+1}=\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(=\left|\sqrt{3}+1\right|=\sqrt{3}+1\)

làm nốt 2 câu cuối nhé, cách làm y trên 

Answer 2

d/\(\sqrt{9+4\sqrt{5}}\)

= \(\sqrt{2^2+4\sqrt{5}+\left(\sqrt{5}\right)^2}\)

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

= \(\left|2+\sqrt{5}\right|\)

=  \(2+\sqrt{5}\)

e/ \(\sqrt{21+4\sqrt{5}}\)

= \(\sqrt{20+4\sqrt{5}+1}\)

=\(\sqrt{\left(2\sqrt{5}\right)^2+2.2\sqrt{5}+1^2}\)

=\(\sqrt{\left(2\sqrt{5}+1\right)^2}\)

= \(\left|2\sqrt{5}+1\right|\)

= \(2\sqrt{5}+1\)