Nội dung bài giảng
Rút gọn rồi tính:
a) \(5\sqrt {{{( - 2)}^4}} \)
b) \( - 4\sqrt {{{( - 3)}^6}} \)
c) \(\sqrt {\sqrt {{{( - 5)}^8}} } \)
d) \(2\sqrt {{{( - 5)}^6}} + 3\sqrt {{{( - 2)}^8}} \)
Gợi ý làm bài
a) \(\eqalign{
& 5\sqrt {{{( - 2)}^4}} = 5\sqrt {{{\left[ {{{( - 2)}^2}} \right]}^2}} \cr
& = 5.\left| {{{( - 2)}^2}} \right| = 5.4 = 20 \cr} \)
b) \(\eqalign{
& - 4\sqrt {{{( - 3)}^6}} = - 4\sqrt {{{\left[ {{{\left( { - 3} \right)}^3}} \right]}^2}} \cr
& = - 4.\left| {{{\left( { - 3} \right)}^3}} \right| = - 4.\left| { - 27} \right| \cr
& = - 4.27 = - 108 \cr} \)
c) \(\eqalign{
& \sqrt {\sqrt {{{( - 5)}^8}} } = \sqrt {\sqrt {{{\left[ {{{\left( { - 5} \right)}^4}} \right]}^2}} } \cr
& = \sqrt {{{( - 5)}^4}} = \sqrt {{{\left[ {{{\left( { - 5} \right)}^2}} \right]}^2}} \cr
& = \left| {{{( - 5)}^2}} \right| = 25 \cr} \)
d) \(\eqalign{
& 2\sqrt {{{( - 5)}^6}} + 3\sqrt {{{( - 2)}^8}} \cr
& = 2.\sqrt {{{\left[ {{{\left( { - 5} \right)}^3}} \right]}^2}} + 3.\sqrt {{{\left[ {{{\left( { - 2} \right)}^4}} \right]}^2}} \cr} \)
\(\eqalign{
& = 2.\left| {{{( - 5)}^3}} \right| + 3.\left| {{{( - 2)}^4}} \right| \cr
& = 2.\left| { - 125} \right| + 3.\left| {16} \right| \cr
& = 2.125 + 3.16 = 298 \cr} \)