Rút gọn rồi tính:
a) \(\sqrt {6,{8^2} - 3,{2^2}} \);
b) \(\sqrt {21,{8^2} - 18,{2^2}} \);
c) \(\sqrt {117,{5^2} - 26,{5^2} - 1440} \);
d) \(\sqrt {146,{5^2} - 109,{5^2} + 27.256} \).
Gợi ý làm bài
a) \(\eqalign{
& \sqrt {6,{8^2} - 3,{2^2}} \cr
& = \sqrt {\left( {6,8 + 3,2} \right)\left( {6,8 - 3,2} \right)} \cr
& = \sqrt {10.3,6} = \sqrt {36} = 6 \cr} \)
b) \(\eqalign{
& \sqrt {21,{8^2} - 18,{2^2}} \cr
& = \sqrt {\left( {21,8 + 18,2} \right)\left( {21,8 - 18,2} \right)} \cr} \)
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\(\eqalign{
& = \sqrt {40.3,6} = \sqrt {4.36} \cr
& = \sqrt 4 .\sqrt {36} = 2.6 = 12 \cr} \)
c) \(\eqalign{
& \sqrt {117,{5^2} - 26,{5^2} - 1440} \cr
& = \sqrt {\left( {117,5 + 26,5} \right)\left( {117,5 - 26,5} \right) - 1440} \cr} \)
\( = \sqrt {144.91 - 1440} = \sqrt {144.\left( {91 - 10} \right)} \)
\( = \sqrt {144.81} = \sqrt {144} .\sqrt {81} = 12.9 = 108\)
d) \(\sqrt {146,{5^2} - 109,{5^2} + 27.256} \)
\( = \sqrt {\left( {144,5 + 109,5} \right)\left( {146,5 - 109,5} \right) + 27.256} \)
\(\eqalign{
& = \sqrt {256.37 + 27.256} \cr
& = \sqrt {256.(36 + 27)} \cr
& = \sqrt {256} .\sqrt {64} = 16.8 = 128 \cr} \)