Question

[Đặng Xuân Vũ]

1. tính

A= căn(4- 2căn3) + căn 27

B= căn(14- 6căn5) + căn125

2. Phân tích thành nhân tử

a, x-4 (x>0)

b, x^2 + 2căn3 . x+3

c, x^2 - 2căn5 . x+5

Answer 1

[DƯƠNG PHAN KHÁNH DƯƠNG]

Bài 1 :

\(A=\sqrt{4-2\sqrt{3}}+\sqrt{27}\)

\(=\sqrt{3-2\sqrt{3}+1}+\sqrt{27}\)

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

\(=\left|\sqrt{3}-1\right|+3\sqrt{3}\)

\(=\sqrt{3}-1+3\sqrt{3}\)

\(=4\sqrt{3}-1\)

\(B=\sqrt{14-6\sqrt{5}}+\sqrt{125}\)

\(=\sqrt{9-6\sqrt{5}+5}+\sqrt{125}\)

\(=\sqrt{\left(3-\sqrt{5}\right)}^2+5\sqrt{5}\)

\(=\left|3-\sqrt{5}\right|+5\sqrt{5}\)

\(=3-\sqrt{5}+5\sqrt{5}\)

\(=3+4\sqrt{5}\)