Why is it important to simplify radical expressions before adding or subtracting, how is adding expressions similar and different from adding polynomials?

Answer by  Joshered (10)

You cannot combine (add or subtract) radicals unless they are like (meaning the numbers under the radicals are the same), such as sqrt(3) + sqrt(3) = 2sqrt(3). Polynomials are expressions, but that do not have absolute value, any roots (such as square roots), or division by a variable. x + 3 is a polynomial, but 5/x + 3 is not.

Answer by  Ascencion (54)

Between the addition signs of a polynomial are only variables which have a coefficient and are raised to some power. This can be any power, including fractional powers. Example: (x-squared) + (sqroot of x). A radical is a fractional power. Simplified radical expressions are ready for placement into a polynomial.

Answer by  VB (361)

You can only combine terms (Add/Subt) if they are the same type of terms. Examples of when you can combine: 4x^2 - x^2 = 3x^3 5 SquareRoot[37] + 3 SquareRoot[37] = 8 SquareRoot[37] Not the same: SquareRoot[72] - SquareRoot[8] But if you simplify, 6 SquareRoot[2] - 2 SquareRoot[2] = 4 SquareRoot[2] then you can combine

Answer by  1pal4u (4)

How are radical and polynomial expressions the same? How are they different?