Question

Rút gọn: \(\dfrac{-3\sqrt{16a}+5a\sqrt{16ab^2}}{2\sqrt{a}}\) (với a > 0, b > 0).

Answer 1

Ta có:

\(\frac{{ - 3\sqrt {16a}  + 5a\sqrt {16a{b^2}} }}{{2\sqrt a }} \\= \frac{{ - 3.\sqrt {16} .\sqrt a  + 5a.\sqrt {16} .\sqrt a .\sqrt {{b^2}} }}{{2\sqrt a }} \\= \frac{{ - 3.4.\sqrt a  + 5a.4.\left| b \right|.\sqrt a }}{{2\sqrt a }}\\= \frac{{ - 3.4.\sqrt a  + 5a.4b\sqrt a }}{{2\sqrt a }}\\ = \frac{{ 4.\sqrt a(-3 + 5ab)}}{{2\sqrt a }} \\= 2(-3+5ab)\\=  - 6 + 10ab\)