radicand

the number inside the radical sign √ ← under the line.

vinculum

a horizontal line placed over a mathematical expression, used to indicate that it is to be considered a group

index

the number over the radical sign √ indicating the root of the radicand.

root

a number indicating the number of repetitive factors needed to obtain the radicand, ie. square root (xx) cube root (xxx).

radical

the check mark part of the radical expression, √ .

roots vs radicals

these terms are opposites and are used to solve equations or inequalities containing them. The square root of 9 is the opposite of 3 squared or (-3) squared.

the sum of radical expressions can be obtained

if and only if the radicands are the same.

The product of a radical expressions can be obtained by

multiplying the radicands of each radical expression.

√(8) times √(2) =√(8)(2) = √16 = 4

√(8) times √(2) =√(8)(2) = √16 = 4

simplifying radicals (square roots only)

1. divide the number inside the radical into two factors, one of which is a perfect square

2. square root the perfect square

3. leave the non-perfect square under the radical

2. square root the perfect square

3. leave the non-perfect square under the radical

How can radical expressions be written without a radical sign?

Change the root to a fraction with the root as the denominator and any exponents on a radicand as the numerator.