Question

What is the simplified form of the following expression? 2√27+√12-3√3-2√12

Answer 1

Answer:

√3

Step-by-step explanation:

The given expression to be simplified is

$2 \sqrt{27}+\sqrt{12}-3\sqrt{3}-2 \sqrt{12}$

but

$2 \sqrt{27}=2\sqrt{9 \times 3}=2 \times \sqrt{9}\times \sqrt{3}=2 \times 3 \times\sqrt{3}=6 \sqrt{3}$

$\sqrt{12}=\sqrt{4\times3}= \sqrt{4}\times \sqrt{3}=2\sqrt{3}$

Since √12=2√3,this implies that,

$2\sqrt{12}=2\times2\sqrt{3}=4 \sqrt{3}$

Therefore,

$2 \sqrt{27}+\sqrt{12}-3\sqrt{3}-2 \sqrt{12}=6\sqrt{3}+2\sqrt{3}-3 \sqrt{3} -4\sqrt{3}$

$=(6+2-3-4)\sqrt{3}$

$=\sqrt{3}$

The simplified form of ,

$2 \sqrt{27}+\sqrt{12}-3\sqrt{3}-2 \sqrt{12}$ is √3