Question

rút gọn các biểu thức sau với x\(\ge\)0

a. \(2\sqrt{3}-4\sqrt{3x}+27-3\sqrt{3x}\)

b.\(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}+28\)

Answer 1

a) \(2\sqrt{3}-4\sqrt{3x}+27-3\sqrt{3x}\)

= \(\left(2\sqrt{3}+27\right)-\left(4\sqrt{3x}+3\sqrt{3x}\right)\)

=\(\sqrt{3}\left(2+3\right)-\sqrt{3x}\left(4-3\right)\)

=\(5\sqrt{3}-\sqrt{3x}\)

=\(\sqrt{3}\left(5-\sqrt{x}\right)\)

b)\(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}+28\)

=\(3\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}+28\)

=\(\sqrt{2x}\left(3-10+21\right)+28\)

=\(14\sqrt{2x}+28\)

=\(14\sqrt{2}\left(\sqrt{x}+\sqrt{2}\right)\)