Câu 13 trang 7 Sách BT Toán 9 Tập 1 Rút gọn rồi tính...

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) $\eqalign{ & 2\sqrt {{{( - 5)}^6}} + 3\sqrt {{{( - 2)}^8}} \cr & = 2.\sqrt {{{\left[ {{{\left( { - 5} \right)}^3}} \right]}^2}} + 3.\sqrt {{{\left[ {{{\left( { - 2} \right)}^4}} \right]}^2}} \cr}$

$\eqalign{ & = 2.\left| {{{( - 5)}^3}} \right| + 3.\left| {{{( - 2)}^4}} \right| \cr & = 2.\left| { - 125} \right| + 3.\left| {16} \right| \cr & = 2.125 + 3.16 = 298 \cr}$