Question

1 Tính

a) \(\sqrt{0.9\times0.16\times0.4}\)

b) \(\sqrt{0,0016}\)

c)\(\frac{\sqrt{72}}{\sqrt{2}}\)

d) \(\frac{\sqrt{2}}{\sqrt{288}}\)

2 Rút gọn

a) \(\frac{2}{a}.\sqrt{\frac{16a^2}{9}}\left(a< 0\right)\)

b) \(\frac{3}{a-1}.\sqrt{\frac{4a^2-8a+4}{25}}\left(a>1\right)\)

c) \(\frac{\sqrt{243a}}{\sqrt{3a}}\left(a>0\right)\)

d) \(\frac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}\left(a\ne0,b\ne0\right)\)

Answer 1

1/ a/ \(\sqrt{0,9.0,16.0,4}=\sqrt{\frac{9.16.4}{10000}}=\sqrt{\frac{\left(3.4.2\right)^2}{10^4}}=\frac{24}{1010}=\frac{6}{25}\)

b/ \(\sqrt{0,0016}=\sqrt{\frac{16}{100}}=\frac{4}{10}=\frac{2}{5}\)

c/ \(\frac{\sqrt{72}}{\sqrt{2}}=\frac{\sqrt{2}.\sqrt{36}}{\sqrt{2}}=\sqrt{36}=6\)

d/ \(\frac{\sqrt{2}}{\sqrt{288}}=\frac{\sqrt{2}}{\sqrt{2}.\sqrt{144}}=\frac{1}{\sqrt{144}}=\frac{1}{12}\)

Answer 2

2.

a/ \(\frac{2}{a}.\sqrt{\frac{16a^2}{9}}=\frac{2}{a}.\frac{4\left|a\right|}{3}=-\frac{8a}{3a}=-\frac{8}{3}\) (Vì a<0)

b/ \(\frac{3}{a-1}.\sqrt{\frac{4a^2-8a+4}{25}}=\frac{3}{a-1}.\sqrt{\frac{4\left(a-1\right)^2}{25}}=\frac{3.2\left|a-1\right|}{5.\left(a-1\right)}=\frac{6\left(a-1\right)}{5\left(a-1\right)}=\frac{6}{5}\)

c/ \(\frac{\sqrt{243a}}{\sqrt{3a}}=\frac{9\sqrt{3a}}{\sqrt{3a}}=9\)

d/ \(\frac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}=\frac{3.3\sqrt{2}.\left|a\right|.\left|b\right|^2}{\sqrt{2}.\left|a\right|.\left|b\right|}=9\left|b\right|\)