Bài 58. Rút gọn các biểu thức sau:
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) \(0,1.\sqrt{200}+2.\sqrt{0,08}+0,4.\sqrt{50}.\)
Hướng dẫn giải:
a)
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\(\eqalign{
& 5\sqrt {{1 \over 5}} + {1 \over 2}\sqrt {20} + \sqrt 5 \cr
& = \sqrt {{{25} \over 5}} + \sqrt {{{20} \over 4}} + \sqrt 5 \cr
& = \sqrt 5 + \sqrt 5 + \sqrt 5 = 3\sqrt 5 \cr} \)
b)
\(\eqalign{
& \sqrt {{1 \over 2} + } \sqrt {4,5} + \sqrt {12,5} \cr
& = \sqrt {{1 \over 2}} + \sqrt {9{1 \over 2}} + \sqrt {25.{1 \over 2}} \cr
& = \sqrt {{1 \over 2}} + 3\sqrt {{1 \over 2}} + 5\sqrt {{1 \over 2}} \cr
& = 9\sqrt {{1 \over 2}} = {{9\sqrt 2 } \over 2} \cr} \)
c)
\(\eqalign{
& \sqrt {20} - \sqrt {45} + 3\sqrt {18} + \sqrt {72} \cr
& = 2\sqrt 5 - 3\sqrt 5 + 3.3\sqrt 2 + 6\sqrt 2 \cr
& = 15\sqrt 2 - \sqrt 5 \cr} \)
d)
\(\eqalign{
& 0,1.\sqrt {200} + 2\sqrt {0,08} + 0,4\sqrt {50} \cr
& = 0,1\sqrt {100.2} + 2\sqrt {2.0,04} + 0,4\sqrt {25.2} \cr
& = \sqrt 2 + 0,4\sqrt 2 + 2\sqrt 2 \cr
& = 3,4\sqrt 2 = {{17\sqrt 2 } \over 5} \cr} \)