Question

Thu gọn biểu thức sau:

\(\left(\sqrt{3}+1\right)\)\(\sqrt{\frac{14-6\sqrt{3}}{5+\sqrt{3}}}\)

Answer 1

mình không viết lại đề nha 

\(=\sqrt{\frac{\left(\sqrt{3}+1\right)^2.\left(14-6\sqrt{3}\right)}{5+\sqrt{3}}}\)

\(=\sqrt{\frac{\left(3+2\sqrt{3}+1\right).\left(14-6\sqrt{3}\right)}{5+\sqrt{3}}}\)

\(=\sqrt{\frac{\left(4+2\sqrt{3}\right).\left(14-6\sqrt{3}\right)}{5+\sqrt{3}}}\)

\(=\sqrt{\frac{56-24\sqrt{3}+28\sqrt{3}-36}{5+\sqrt{3}}}\)

\(=\sqrt{\frac{20+4\sqrt{3}}{5+\sqrt{3}}}\)

\(=\sqrt{\frac{\left(20+4\sqrt{3}\right).\left(5-\sqrt{3}\right)}{\left(5+\sqrt{3}\right).\left(5-\sqrt{3}\right)}}\)

\(=\sqrt{\frac{100-20\sqrt{3}+20\sqrt{3}-12}{5^2-\sqrt{3}^2}}\)

\(=\sqrt{\frac{88}{25-3}}\)

\(=\sqrt{\frac{88}{22}}\)

\(=\sqrt{4}\)

\(=2\)

HỌC TỐT !!!