Question

Đưa bth sau về dạng bình phương của 1 số thực:

a, \(9+4\sqrt{5}\)

b, \(23-8\sqrt{7}\)

c, \(4-2\sqrt{3}\)

d, \(11+6\sqrt{2}\)

Answer 1

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

b) \(23-8\sqrt{7}=4^2-2.4.\sqrt{7}+\left(\sqrt{7}\right)^2=\left(4-\sqrt{7}\right)^2\)

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

d) \(11+6\sqrt{2}=3^2+2.3.\sqrt{2}+\left(\sqrt{2}\right)^2=\left(3+\sqrt{2}\right)^2\)

Answer 2

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

b) \(23-8\sqrt{7}=\left(4-\sqrt{7}\right)^2\)

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

d) \(11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)