Question

Viết các biểu thức sau dưới dạng bình phương

a, \(21-8\sqrt{5}\)

b, \(47-12\sqrt{11}\)

c,\(13-4\sqrt{3}\)

d,\(43+30\sqrt{2}\)

e, \(41+24\sqrt{2}\)

g,\(29-12\sqrt{5}\)

h \(49-8\sqrt{3}\)

i, \(37-12\sqrt{7}\)

Answer 1

a) \(21-8\sqrt{5}=16-2\times4\times\sqrt{5}+5=\left(4-\sqrt{5}\right)^2\)

b) \(47-12\sqrt{11}=36-2\times6\times\sqrt{11}+11=\left(6-\sqrt{11}\right)^2\)

c) \(13-4\sqrt{3}=12-2\times1\times\sqrt{3}+1=\left(2\sqrt{3}-1\right)^2\)

d) \(43+30\sqrt{2}=25+2\times5\times3\sqrt{2}+18=\left(5+3\sqrt{2}\right)^2\)

e) \(41+24\sqrt{2}=9+2\times3\times4\sqrt{2}+32=\left(3+4\sqrt{2}\right)^2\)

g) \(29-12\sqrt{5}=9+2\times3\times2\sqrt{5}+20=\left(3+2\sqrt{5}\right)^2\)

h) \(49-8\sqrt{3}=48-2\times4\sqrt{3}\times1+1=\left(4\sqrt{3}-1\right)^2\)

i) \(37-12\sqrt{7}=28-2\times3\times2\sqrt{7}+9=\left(2\sqrt{7}-3\right)^2\)