Question

câu b, c, d thôi ạ!

Answer 1

c: \(=\left(4+\sqrt{3}\right)\cdot\sqrt{\left(4-\sqrt{3}\right)^2}\)

=(4+căn 3)(4-căn 3)

=16-3=13

d: \(=\sqrt{6+2\sqrt{5-2\sqrt{3}-1}}\)

\(=\sqrt{6+2\cdot\sqrt{4-2\sqrt{3}}}\)

\(=\sqrt{6+2\cdot\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)

Answer 2

b) \(\sqrt{\left(1-\sqrt{5}\right)^2}+\sqrt{23-8\sqrt{5}}\)

\(=\left|1-\sqrt{5}\right|+\sqrt{23-2\sqrt{60}}\)

\(=\sqrt{5}-1+\sqrt{\left(\sqrt{20}\right)^2-2.\sqrt{20}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)

\(=\sqrt{5}-1+\sqrt{\left(\sqrt{20}-\sqrt{3}\right)^2}\)

\(=\sqrt{5}-1+\sqrt{20}-\sqrt{3}=\sqrt{5}+2\sqrt{5}-1-\sqrt{3}\)

\(=3\sqrt{5}-1-\sqrt{3}\)