Question

Rút gọn các biểu thức sau ( biết a > 0, b > 0 ):

a) \(5\sqrt{a}-3\sqrt{25a^3}+2\sqrt{36ab^2}-2\sqrt{9a}\)

b) \(\sqrt{64ab^3}-3\sqrt{12a^3b^3}+2ab\sqrt{9ab}-5b\sqrt{81a^3}b\)

Answer 1

a) Ta có: \(5\sqrt{a}-3\sqrt{25a^3}+2\sqrt{36ab^2}-2\sqrt{9a}\)

\(=5\sqrt{a}-15a\sqrt{a}+12b\sqrt{a}-6\sqrt{a}\)

\(=-\sqrt{a}-15a\sqrt{a}+12\sqrt{a}b\)

b) Ta có: \(\sqrt{64ab^3}-3\sqrt{12a^3b^3}+2ab\sqrt{9ab}-5b\sqrt{81a^3b}\)

\(=8b\sqrt{a}-6ab\sqrt{3ab}+6ab\sqrt{ab}-45a^2b\sqrt{ab}\)

Answer 2

a)\(5\sqrt{a}-3\sqrt{25a^3}+2\sqrt{36ab^2}-2\sqrt{9a}=5\sqrt{a}-15\left|a\right|\sqrt{a}+12\left|b\right|\sqrt{a}-6\sqrt{a}=-\sqrt{a}-15a\sqrt{a}+12b\sqrt{a}\)

b)\(\sqrt{64ab^3}-3\sqrt{12a^3b^3}+2ab\sqrt{9ab}-5b\sqrt{81a^3b}\)

\(=8\left|b\right|\sqrt{ab}-6\left|ab\right|\sqrt{3ab}+6ab\sqrt{ab}-45b\left|a\right|\sqrt{ab}\)

\(=8b\sqrt{ab}-6ab\sqrt{3ab}+6ab\sqrt{ab}-45ab\sqrt{ab}\)

\(=8b\sqrt{ab}-6ab\sqrt{3ab}-39ab\sqrt{ab}\)

Answer 3