Question

Bài 4 Rút gọn

a) sqrt(4 - 2sqrt(3))

d) sqrt(9 + 4sqrt(2))

g) sqrt19 - 8sqrt(3)

b)

e)

sqrt(3 + 2sqrt(2))

sqrt(6 + 2sqrt(5))

h) sqrt(22 - 12sqrt(2))

sqrt(9 + 4sqrt(5))

i) sqrt(29) - 12sqrt(5)

sqrt(16 - 6sqrt(7))

Answer 1

a) \(\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\)

d) \(\sqrt{9+4\sqrt{2}}=\sqrt{\left(2\sqrt{2}\right)^2+4\sqrt{2}+1}=\sqrt{\left(2\sqrt{2}+1\right)^2}=\left|2\sqrt{2}+1\right|=2\sqrt{2}+1\)

b) \(\sqrt{3+2\sqrt{2}}=\sqrt{\left(\sqrt{2}\right)^2+2\sqrt{2}+1}=\sqrt{\left(\sqrt{2}+1\right)^2}=\left|\sqrt{2}+1\right|=\sqrt{2}+1\)

\(\sqrt{6+2\sqrt{5}}=\sqrt{\left(\sqrt{5}\right)^2+2\sqrt{5}+1}=\sqrt{\left(\sqrt{5}+1\right)^2}=\left|\sqrt{5}+1\right|=\sqrt{5}+1\)

\(\sqrt{22-12\sqrt{2}}=\sqrt{\left(3\sqrt{2}\right)^2-2.3\sqrt{2}.2+2^2}=\sqrt{\left(3\sqrt{2}-2\right)^2}=\left|3\sqrt{2}-2\right|=3\sqrt{2}-2\)

\(\sqrt{9+4\sqrt{5}}=\sqrt{\left(\sqrt{5}\right)^2+2.\sqrt{5}.2+2^2}=\sqrt{\left(\sqrt{5}+2\right)^2}=\left|\sqrt{5}+2\right|=\sqrt{5}+2\)

\(\sqrt{29-12\sqrt{5}}=\sqrt{\left(2\sqrt{5}\right)^2-2.2\sqrt{5}.3+3^2}=\sqrt{\left(2\sqrt{5}-3\right)^2}=\left|2\sqrt{5}-3\right|=2\sqrt{5}-3\)

\(\sqrt{16-6\sqrt{7}}=\sqrt{3^2-2.3.\sqrt{7}+\left(\sqrt{7}\right)^2}=\sqrt{\left(3-\sqrt{7}\right)^2}=\left|3-\sqrt{7}\right|=3-\sqrt{7}\)