SOLUTION: Add or subtract 4(the square root of)7 – 2(the square root of)7 + 4(the square root of)7. Simplify by collecting like radical terms if possible.

Algebra ->  Square-cubic-other-roots -> SOLUTION: Add or subtract 4(the square root of)7 – 2(the square root of)7 + 4(the square root of)7. Simplify by collecting like radical terms if possible.      Log On


   

Question 401442: Add or subtract 4(the square root of)7 – 2(the square root of)7 + 4(the square root of)7. Simplify by collecting like radical terms if possible.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
4sqrt%287%29-2sqrt%287%29%2B4sqrt%287%29
Like radical terms are terms where the radical(s) all have the same index and radicand. ("radicand" is the expression inside a radical.) All of your terms are square roots (whose implied index is 2) so the indices are the same. And the radicands are all 7's. So all these terms are like radical terms.

To add or subtract like radical terms you just add or subtract the coefficients. It is just like adding/subtracting variable terms! So adding/subtracting
4sqrt%287%29-2sqrt%287%29%2B4sqrt%287%29
is just like adding/subtracting
4x - 2x + 4x
So just like
4x - 2x + 4x = 6x
4sqrt%287%29-2sqrt%287%29%2B4sqrt%287%29+=+6sqrt%287%29
Note then when adding/subtracting radical terms, nothing changes with the radicals. Only the coefficient get added/subtracted.