Question

Bài 1: Rút gọn căn bậc 2 theo hằng đẳng thức 1:

a)\(\sqrt{\left(23-15\sqrt{3}\right)^2}\)

b) \(\sqrt{\left(2-2\sqrt{3}\right)^2}\)

c) \(\sqrt{\left(15-4\sqrt{3}\right)^2}\)

d)\(\sqrt{\left(16-6\sqrt{7}\right)^2}\)

f)\(\sqrt{\left(22-8\sqrt{3}\right)^2}\)

g) \(\sqrt{\left(9-4\sqrt{2}\right)^2}\)

h) \(\sqrt{\left(13-4\sqrt{3}\right)^2}\)

i)\(\sqrt{\left(7-3\sqrt{3}\right)^2}\)

(mink đag cần gấp)

Answer 1

Bài 1:

a) Ta có: \(\sqrt{\left(23-15\sqrt{3}\right)^2}\)

\(=\left|23-15\sqrt{3}\right|\)

\(=\left|\sqrt{529}-\sqrt{675}\right|\)

\(=\sqrt{675}-\sqrt{529}\)

\(=15\sqrt{3}-23\)

b) Ta có: \(\sqrt{\left(2-2\sqrt{3}\right)^2}\)

\(=\left|2-2\sqrt{3}\right|\)

\(=2\sqrt{3}-2\)

c) Ta có: \(\sqrt{\left(15-4\sqrt{3}\right)^2}\)

\(=\left|15-4\sqrt{3}\right|\)

\(=15-4\sqrt{3}\)

d) Ta có: \(\sqrt{\left(16-6\sqrt{7}\right)^2}\)

\(=\left|16-6\sqrt{7}\right|\)

\(=\left|\sqrt{256}-\sqrt{252}\right|\)

\(=16-6\sqrt{7}\)

f) Ta có: \(\sqrt{\left(22-8\sqrt{3}\right)^2}\)

\(=\left|22-8\sqrt{3}\right|\)

\(=\left|\sqrt{484}-\sqrt{192}\right|\)

\(=22-8\sqrt{3}\)

g) Ta có: \(\sqrt{\left(9-4\sqrt{2}\right)^2}\)

\(=\left|9-4\sqrt{2}\right|\)

\(=9-4\sqrt{2}\)

h) Ta có: \(\sqrt{\left(13-4\sqrt{3}\right)^2}\)

\(=\left|13-4\sqrt{3}\right|\)

\(=13-4\sqrt{3}\)

i) Ta có: \(\sqrt{\left(7-3\sqrt{3}\right)^2}\)

\(=\left|7-3\sqrt{3}\right|\)

\(=7-3\sqrt{3}\)