Question

1)Tính (Áp dụng \(\sqrt{\dfrac{A}{B}}=\sqrt{\dfrac{A}{B}}\)và ngược lại cho A≥0,B>0)

a)\(\sqrt{\dfrac{361}{144}}\)

b)\(\sqrt{\dfrac{4,9}{16,9}}\)

c)\(\dfrac{\sqrt{18}}{\sqrt{450}}\)

d)\(\dfrac{\sqrt{6^5}}{\sqrt{2^3.3^5}}\)

Answer 1

a) \(\sqrt{\dfrac{361}{144}}=\dfrac{\sqrt{362}}{\sqrt{144}}=\dfrac{19}{12}\)

b) \(\sqrt{\dfrac{4,9}{16,9}}=\sqrt{\dfrac{4,9.10}{16,9.10}}=\sqrt{\dfrac{49}{169}}=\dfrac{\sqrt{49}}{\sqrt{169}}=\dfrac{7}{13}\)

c) \(\dfrac{\sqrt{18}}{\sqrt{450}}=\sqrt{\dfrac{18}{450}}=\sqrt{\dfrac{1}{25}}=\dfrac{\sqrt{1}}{\sqrt{25}}=\dfrac{1}{5}\)

d) \(\dfrac{\sqrt{6^5}}{\sqrt{2^3.3^5}}=\sqrt{\dfrac{6^5}{2^3.3^5}}=\sqrt{\dfrac{2^5}{2^3}}=\sqrt{2^2}=2\)