Question

Which choice is equivalent to the expression below?

√12-√27+√75

A.21√3
B.9√3
C.5√3
D.4√3

Answer 1

$\sqrt{12}-\sqrt{27}+\sqrt{75}=\sqrt{4\cdot3}-\sqrt{9\cdot3}+\sqrt{25\cdot3}\\\\=\sqrt4\cdot\sqrt3-\sqrt9\cdot\sqrt3+\sqrt{25}\cdot\sqrt3=2\sqrt3-3\sqrt3+5\sqrt3=4\sqrt3\\\\Answer:D.$

Answer 2

$\sqrt{12} - \sqrt{27} + \sqrt{75} = \sqrt{4*3} - \sqrt{9*3} + \sqrt{25*3} = \\\\=2\sqrt{ 3} -3\sqrt{ 3} + 5\sqrt{ 3} = 4 \sqrt3}$

$Answer : \ \ D. \ \ 4 \sqrt{3}$