Question

Rút gọn biểu thức

a. \(\left(2\sqrt{5}-\sqrt{7}\right)\left(2\sqrt{5}+\sqrt{7}\right)\)

b.\(\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)\)

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

d. \(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}\)

e. \(\sqrt{55-6\sqrt{6}}\)

f. \(\sqrt{21-6\sqrt{6}}\)

Answer 1

Ta có :

a)\(\left(2\sqrt{5}-\sqrt{7}\right)\left(2\sqrt{5}-\sqrt{7}\right)=\left(2\sqrt{5}\right)^2-\left(\sqrt{7}\right)^2=20-7=13\)

b)\(\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)=\left(2\sqrt{3}\right)^2-\left(5\sqrt{2}\right)^2=12-50=-38\)

c)\(\sqrt{9+4\sqrt{5}}=\sqrt{2^2+2.2.\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(2+\sqrt{5}\right)^2}=\left|2+\sqrt{5}\right|=2+\sqrt{5}\)