Algebraically, you have to factor the square root of 7 to see why you're wrong:
[tex] 3\sqrt{7}-\sqrt{7} = \sqrt{7}(3-1) = 2\sqrt{7} [/tex]
Conceptually, think that any object - say an apple - represents the square root of seven.
So, you have three apples, and you take away one apple. You have two apples remaining, i.e. [tex] 2\sqrt{7} [/tex]
[tex]3\sqrt{7} - \sqrt{7}[/tex]
Let x represent [tex]\sqrt{7}[/tex], then you can rewrite the expression as 3x - x.
3x - x = 2x. Now replace "x" with [tex]\sqrt{7}[/tex] and you get 2[tex]\sqrt{7}[/tex].
The reason 3 is incorrect is because you are supposed to perform the operation (+, -, x, ÷) with the coefficients, not with the variable or radical.
