Rút gọn các biểu thức sau: 5 căn 1/5 +1/2 . căn 20 + căn 5

Giải Toán 9 Bài 8: Rút gọn biểu thức căn bậc hai

Bài 58 trang 32 Toán lớp 9 Tập 1: 

a) $5\sqrt{\frac{1}{5}}+\frac{1}{2}.\sqrt{20}+\sqrt{5}$

b) $\sqrt{\frac{1}{2}}+\sqrt{4,5}+\sqrt{12,5}$

c) $\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}$

d) $0,1.\sqrt{200}+2.\sqrt{0,08}+0,4.\sqrt{50}$

Lời giải:

a)

$5\sqrt{\frac{1}{5}}+\frac{1}{2}.\sqrt{20}+\sqrt{5}=\sqrt{5^2.\frac{1}{5}}+\sqrt{{\left(\frac{1}{2}\right)}^2.20}+\sqrt{5}=\sqrt{5}+\sqrt{\frac{1}{4}.20}+\sqrt{5}=\sqrt{5}+\sqrt{5}+\sqrt{5}=3\sqrt{5}$

b)

$\sqrt{\frac{1}{2}}+\sqrt{4,5}+\sqrt{12,5}=\sqrt{\frac{1}{2}}+\sqrt{\frac{9}{2}}+\sqrt{\frac{25}{2}}=\sqrt{\frac{1}{2}}+\sqrt{3^2.\frac{1}{2}}+\sqrt{5^2.\frac{1}{2}}=\sqrt{\frac{1}{2}}+3\sqrt{\frac{1}{2}}+5\sqrt{\frac{1}{2}}=9\sqrt{\frac{1}{2}}=9.\frac{\sqrt{1}}{\sqrt{2}}=\frac{9.\sqrt{2}}{\sqrt{2}.\sqrt{2}}=\frac{9.\sqrt{2}}{2}$

c)

$\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}=\sqrt{4.5}-\sqrt{9.5}+3\sqrt{9.2}+\sqrt{\mathrm{9.4.2}}=\sqrt{4}.\sqrt{5}-\sqrt{9}.\sqrt{5}+3.\sqrt{9}.\sqrt{2}+\sqrt{9}.\sqrt{4}.\sqrt{2}=2\sqrt{5}-3\sqrt{5}+\mathrm{3.3.}\sqrt{2}+\mathrm{3.2.}\sqrt{2}=-\sqrt{5}+9\sqrt{2}+6\sqrt{2}=-\sqrt{5}+15\sqrt{2}$

d) 

$0,1.\sqrt{200}+2.\sqrt{0,08}+0,4.\sqrt{50}=0,1.\sqrt{100.2}+2.\sqrt{\frac{8}{100}}+0,4.\sqrt{25.2}=0,\mathrm{1.10.}\sqrt{2}+2.\frac{\sqrt{4.2}}{\sqrt{100}}+0,\mathrm{4.5.}\sqrt{2}=\sqrt{2}+\frac{\mathrm{2.2.}\sqrt{2}}{10}+2\sqrt{2}=\frac{17\sqrt{2}}{5}$