Question

tính

a)\(\frac{\sqrt{10}+\sqrt{6}}{2\sqrt{5}+\sqrt{12}}\)

b)\(\sqrt{\frac{16}{81}}\)

c)\(\sqrt{2\frac{7}{9}}\)

d)\(\frac{\sqrt{2}}{\sqrt{288}}\)

f)\(\sqrt{1\frac{7}{9}.0,04}\)

g)\(\sqrt{0,09.1,21-0,09.0,4}\)

h)\(\left(3\sqrt{18}-2\sqrt{98}+\sqrt{72}\right):\sqrt{2}\)

i)\(\left(\sqrt{27}-6\sqrt{243}\right):3\sqrt{3}\)

Answer 1

a) \(\frac{\sqrt{2}}{2}\)

b)\(\frac{4}{9}\)

c)\(\frac{5}{3}\)

d)\(\frac{1}{12}\)

f) \(\frac{4}{15}\)

g) \(\frac{27}{100}\)

h) 2

i) -17

Answer 2

a) \(\frac{\sqrt{2}}{2}\)

b) \(\frac{4}{9}\)

c) \(\frac{5}{3}\)

d) \(\frac{1}{12}\)

f) \(\frac{4}{15}\)

g) \(\frac{27}{100}\)

h) 1

i) -17

Cách làm: Bấm máy tính (Nhanh, hiệu quả)

Answer 3

a, \(\frac{\sqrt{10}+\sqrt{6}}{2\sqrt{5}+\sqrt{12}}=\frac{\sqrt{2}\sqrt{5}+\sqrt{2}\sqrt{3}}{2\sqrt{5}+2\sqrt{3}}=\frac{\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)}{2\left(\sqrt{5}+\sqrt{3}\right)}=\frac{\sqrt{2}}{2}\)

b, \(\sqrt{\frac{16}{81}}=\frac{\sqrt{16}}{\sqrt{81}}=\frac{4}{9}\)

c, \(\sqrt{2\frac{7}{9}}=\sqrt{\frac{25}{9}}=\frac{\sqrt{25}}{\sqrt{9}}=\frac{5}{3}\)

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

f

\(\sqrt{1\frac{7}{9}.0,04}=\sqrt{\frac{16}{9}.0,04}=\sqrt{\frac{16}{9}}\sqrt{0,04}=\frac{\sqrt{16}}{\sqrt{9}}.\sqrt{0,04}=\frac{4}{3}.0,2=\frac{4}{15}\) g, \(\sqrt{0,09.1,12-0,09.0,4}=\sqrt{0,09\left(1,12-0,4\right)}=\sqrt{0,09.0,72}=\frac{9\sqrt{2}}{50}\)

h, \(\frac{3\sqrt{18}-2\sqrt{98}+\sqrt{72}}{\sqrt{2}}=\frac{9\sqrt{2}-14\sqrt{2}+6\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}\left(9-14+6\right)}{\sqrt{2}}=9-14+6=1\)

i, \(\frac{\sqrt{27}-6\sqrt{243}}{3\sqrt{3}}=\frac{3\sqrt{3}-3\sqrt{3}.18}{3\sqrt{3}}=\frac{3\sqrt{3}\left(1-18\right)}{3\sqrt{3}}=1-18=-17\)