1. Rút gọn biểu thức:
a)\(\sqrt{\dfrac{81}{25}.\dfrac{49}{16}.\dfrac{9}{196}}\)
b)\(\sqrt{72}-5\sqrt{2}-\sqrt{49.3}+\sqrt{48}+\sqrt{12}\)
c)\(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(2+\sqrt{3}\right)^2}\)
d)\(\sqrt{5}+\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\)
2. Cho tam giác ABC có AB =6cm, AC=4,5cm, BC=7,5cm
a) CM tam giác ABC vuông tại A
b)Tính các góc B,C và đường cao AH của tam giác đó
1. Rút gọn biểu thức:
a) \(\sqrt{\dfrac{81}{25}.\dfrac{49}{16}.\dfrac{9}{196}}=\sqrt{\dfrac{81}{25}}.\sqrt{\dfrac{49}{16}}.\sqrt{\dfrac{9}{4.49}}=\dfrac{9}{5}.\dfrac{7}{4}.\dfrac{3}{2.7}=\dfrac{9.3}{5.4.2}=\dfrac{27}{40}\)
b) \(\sqrt{72}-5\sqrt{2}-\sqrt{49.3}+\sqrt{48}+\sqrt{12}=\)
\(=\sqrt{9.4.2}-5\sqrt{2}-\sqrt{49.3}+\sqrt{16.3}+\sqrt{4.3}\)
\(=3.2\sqrt{2}-5\sqrt{2}-7\sqrt{3}+4\sqrt{3}+2\sqrt{3}\)
\(=6\sqrt{2}-5\sqrt{2}-7\sqrt{3}+4\sqrt{3}+2\sqrt{3}\)
\(=\sqrt{2}-\sqrt{3}\)
c) \(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(2+\sqrt{3}\right)^2}=\) \(=\left|2-\sqrt{3}\right|+\left|2+\sqrt{3}\right|=2-\sqrt{3}+2+\sqrt{3}=4\)
d) \(\sqrt{5}+\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}=\)
\(=\sqrt{5}+\sqrt{4.5}-\sqrt{9.5}+3\sqrt{9.2}+\sqrt{9.4.2}\)
\(=\sqrt{5}+2\sqrt{5}-3\sqrt{5}+3.3\sqrt{2}+3.2\sqrt{2}\)
\(=\sqrt{5}+2\sqrt{5}-3\sqrt{5}+9\sqrt{2}+6\sqrt{2}\)
\(=15\sqrt{2}\)
