Question

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

Answer 1

√3

Explanation:

The given expression to be simplified is

`2 √(27)+√(12)-3√(3)-2 √(12)`

but

`2 √(27)=2√(9 * 3)=2 * √(9)* √(3)=2 * 3 *√(3)=6 √(3)`

`√(12)=√(4*3)= √(4)* √(3)=2√(3)`

Since √12=2√3,this implies that,

`2√(12)=2*2√(3)=4 √(3)`

Therefore,

`2 √(27)+√(12)-3√(3)-2 √(12)=6√(3)+2√(3)-3 √(3) -4√(3)`

`=(6+2-3-4)√(3)`

`=√(3)`

The simplified form of ,

`2 √(27)+√(12)-3√(3)-2 √(12)` is √3