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√(7)-√(7) = √(7)(3-1) = 2√(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√(7)`

Answer 2

`3√(7) - √(7)`

Let x represent
`√(7)`, then you can rewrite the expression as 3x - x.

3x - x = 2x. Now replace "x" with
`√(7)` and you get 2
`√(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.