Question

Khử mẫu số trong căn thức sau: \(-4\sqrt{\frac{\sqrt{3}-1}{2+\sqrt{3}}}\)

cho minhf hỏi là kết quả = bao nhiêu

Answer 1

ta có :

\(-4\sqrt{\frac{\sqrt{3}-1}{2+\sqrt{3}}}=-4\sqrt{\frac{\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)}{\left(2+\sqrt{3}\right)^2}}=-\frac{4\sqrt{1+\sqrt{3}}}{\left(2+\sqrt{3}\right)}=-\frac{2\sqrt{4+4\sqrt{3}}}{\left(2+\sqrt{3}\right)}\)

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

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

Answer 2

\(-4\sqrt{\frac{\sqrt{3}-1}{2+\sqrt{3}}}\)

\(-4\sqrt{\frac{\left(\sqrt{3}-1\right)\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}}\)

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

\(=-\left(4\sqrt{3\sqrt{3}-5}\right)\)

\(=-\sqrt{48\sqrt{3}-80}\)

Answer 3

\(-4\sqrt{\frac{\sqrt{3}-1}{2+\sqrt{3}}}=-4\sqrt{\frac{\left(\sqrt{3}-1\right)\left(2-\sqrt{3}\right)}{4-1}}\)

\(=-4\sqrt{2\sqrt{3}-3-2+\sqrt{3}}=-4\sqrt{3\sqrt{3}-5}\)