Question

Rút gọn:

a. 11 + 2\(\sqrt{30}\)

b. 10 + 2\(\sqrt{21}\)

c. 6x - \(\sqrt{x}-1\)

d. 11 - 2\(\sqrt{45}\)

e. 4x - 3\(\sqrt{x}\) - 1

j. 12 - 2\(\sqrt{27}\)

Answer 1

\(a.11+2\sqrt{30}=6+2.\sqrt{6}.\sqrt{5}+5=\left(\sqrt{6}+\sqrt{5}\right)^2\)

\(b.10+2\sqrt{21}=7+2\sqrt{7}.\sqrt{3}+3=\left(\sqrt{7}+\sqrt{3}\right)^2\)

\(c.6x-\sqrt{x}-1=6x+2\sqrt{x}-3\sqrt{x}-1=2\sqrt{x}\left(3\sqrt{x}+1\right)-\left(3\sqrt{x}+1\right)=\left(3\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)\) \(d.14-2\sqrt{45}=14-6\sqrt{5}=9-2.3\sqrt{5}+5=\left(3-\sqrt{5}\right)^2\)

\(e.4x-3\sqrt{x}-1=4x-4\sqrt{x}+\sqrt{x}-1=4\sqrt{x}\left(\sqrt{x}-1\right)+\left(\sqrt{x}-1\right)=\left(\sqrt{x}-1\right)\left(4\sqrt{x}+1\right)\) \(j.12-2\sqrt{27}=9-2.3.\sqrt{3}+3=\left(3-\sqrt{3}\right)^2\)