Question

[Thao Nguyen]

Đưa các biểu thức về dạng bình phương :

a) 3+ 2\(\sqrt{2}\)

b) 3-\(\sqrt{8}\)

c) 9+ 4\(\sqrt{5}\)

d) 23- 8\(\sqrt{7}\)

Answer 1

[Tri Nguyen]

a/ 3 + 2\(\sqrt{2}\) = 2 + 2\(\sqrt{2}\) + 1 = \(\sqrt{2}^2\) + 2\(\sqrt{2}\) + 1² = ( \(\sqrt{2}\) + 1 )²

b/ 3 - \(\sqrt{8}\) = 2 - \(\sqrt{4.2}\) + 1 = 2 - 2\(\sqrt{2}\) + 1 = \(\sqrt{2}^2\) - 2\(\sqrt{2}\) + 1²

= ( \(\sqrt{2}\) - 1 )²

c/ 9 + 4\(\sqrt{5}\) = 4 + 2.2\(\sqrt{5}\) + 5 = 2² + 2.2\(\sqrt{5}\) + \(\sqrt{5}\)²

= ( 2 + \(\sqrt{5}\) )²

d/ 23 - 8\(\sqrt{7}\) = 16 - 2.4.\(\sqrt{7}\) + 7 = 4² - 2.4.\(\sqrt{7}\) + \(\sqrt{7}^2\)

= ( 4 - \(\sqrt{7}\) )²