Question

rút gọn các biểu thức sau :

A = \(\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)

B=\(\dfrac{9\sqrt{3}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}\)

C=\(\sqrt{5-2\sqrt{6}}\)

2)Tính

a) \(\left(\sqrt{12}+3\sqrt{15}-4\sqrt{135}\right)\sqrt{3}\)

ai giải giúp e mấy câu này với e cần lắm ạ !!!

Answer 1

Bài 1:

\(A=\dfrac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}=\dfrac{\sqrt{2}\left(\sqrt{3}+\sqrt{7}\right)}{2\sqrt{3}+2\sqrt{7}}\)

\(=\dfrac{\sqrt{2}\left(\sqrt{3}+\sqrt{7}\right)}{2\left(\sqrt{3}+\sqrt{7}\right)}=\dfrac{\sqrt{2}}{2}\)

\(B=\dfrac{9\sqrt{3}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}=\dfrac{9\sqrt{3}+9\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)

\(=\dfrac{18\sqrt{3}}{\sqrt{5}+\sqrt{3}}\)

\(C=\sqrt{5-2\sqrt{6}}=\sqrt{3-2\sqrt{6}+2}\)

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

Bài 2:

\(\left(\sqrt{12}+3\sqrt{15}+4\sqrt{135}\right)\sqrt{3}\)

\(=6+9\sqrt{5}+36\sqrt{5}\)

\(=6+45\sqrt{5}\)