Question

[Quỳnh Nguyễn]

B1 : Rút gọn :

\(6xy.\sqrt{\frac{9x^2}{16y^2}}\) \(\left(x< 0;y\ne0\right)\)

\(\sqrt{\frac{4+20a+25a^2}{b^4}}\)\(\left(b< 0;a\ge\frac{-2}{5}\right)\)

\(\left(m-n\right).\sqrt{\frac{m-n}{\left(m-n\right)^2}}\)\(\left(0< m< n\right)\)

B2 : Tính :

\(1.\left(2\sqrt{3}-\sqrt{12}\right):5\sqrt{3}\)

\(2.\sqrt{\frac{317^2-302^2}{1013^2-1012^2}}\)

\(3.\sqrt{27\left(1-\sqrt{3}\right)^2}:3\sqrt{75}\)

\(4.\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}}+\sqrt{5}\right):2\sqrt{5}\)

Answer 1

[Minh Nguyen]

Bài 1 :

\(6xy\cdot\sqrt{\frac{9x^2}{16y^2}}=6xy\cdot\frac{3x}{4y}=\frac{18x^2y}{4y}=\frac{9}{2}x^2\)

\(\sqrt{\frac{4+20a+25a^2}{b^4}}=\sqrt{\frac{\left(2+5a\right)^2}{\left(b^2\right)^2}}=\frac{2+5a}{b^2}\)

\(\left(m-n\right).\sqrt{\frac{m-n}{\left(m-n\right)^2}}=\sqrt{\left(m-n\right)^2}\cdot\sqrt{\frac{1}{m-n}}=\sqrt{\frac{\left(m-n\right)^2}{m-n}}=\sqrt{m-n}\)

Bài 2 : 

1. \(\left(2\sqrt{3}-\sqrt{12}\right):5\sqrt{3}=\left(2\sqrt{3}-2\sqrt{3}\right):5\sqrt{3}=0:5\sqrt{3}=0\)

2. \(\sqrt{\frac{317^2-302^2}{1013^2-1012^2}}=\frac{\sqrt{\left(317+302\right)\left(317-302\right)}}{\sqrt{\left(1013+1012\right)\left(1013-1012\right)}}=\frac{\sqrt{619}\cdot\sqrt{15}}{\sqrt{2025}}=\sqrt{\frac{619}{135}}\)(check lại)

3. \(\sqrt{27\left(1-\sqrt{3}\right)^2}:3\sqrt{75}\)

\(=\sqrt{27}\left(1-\sqrt{3}\right):15\sqrt{3}\)

\(=3\sqrt{3}\left(1-\sqrt{3}\right):15\sqrt{3}\)

\(=\frac{1-\sqrt{3}}{5}\)

4.\(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}}+\sqrt{5}\right):2\sqrt{5}\)

\(=\left(\frac{5}{\sqrt{5}}+\frac{\sqrt{20}}{2}-\frac{\frac{5}{4}\cdot2}{\sqrt{5}}+\sqrt{5}\right):2\sqrt{5}\)

\(=\left(\sqrt{5}+\frac{2\sqrt{5}}{2}-\frac{\frac{5}{2}}{\sqrt{5}}+\sqrt{5}\right):2\sqrt{5}\)

\(=\left(\sqrt{5}+\sqrt{5}+\frac{\sqrt{5}}{2}+\sqrt{5}\right):2\sqrt{5}\)

\(=\frac{7}{2}\sqrt{5}:2\sqrt{5}\)

\(=\frac{7}{4}\)