Question

3 radical 7 - radical 7 = 3 why is this incorrect?

Answer 1

Algebraically, you have to factor the square root of 7 to see why you're wrong:

$3\sqrt{7}-\sqrt{7} = \sqrt{7}(3-1) = 2\sqrt{7}$

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. $2\sqrt{7}$

Answer 2

$3\sqrt{7} - \sqrt{7}$

Let x represent $\sqrt{7}$, then you can rewrite the expression as 3x - x.

3x - x = 2x.  Now replace "x" with  $\sqrt{7}$ and you get 2$\sqrt{7}$.

The reason 3 is incorrect is because you are supposed to perform the operation (+, -, x, ÷) with the coefficients, not with the variable or radical.