Question

So sánh:

a) \(\sqrt{3^2.11}\) và \(3\sqrt{11}\);                         b) \(\sqrt{\left(-5\right)^2.2}\) và \(-\left(-5\sqrt{2}\right)\).

Answer 1

a. Ta có: \(\sqrt {{3^2}.11}  = \sqrt {{3^2}} .\sqrt {11}  = 3\sqrt {11} \).

b. Ta có: \(\sqrt {{{\left( { - 5} \right)}^2}.2}  = \sqrt {{{\left( { - 5} \right)}^2}} .\sqrt 2  = 5\sqrt 2 \)

\( - \left( { - 5\sqrt 2 } \right) = 5\sqrt 2 \).

Vậy \(\sqrt {{{\left( { - 5} \right)}^2}.2}  =  - \left( { - 5\sqrt 2 } \right)\).