Add/Subtract Radicals (9.04)

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root, cube root, etc. It is typically represented using the radical symbol (√) or (∛) for cube roots.

Front

How do you simplify a square root?

Back

To simplify a square root, factor the number under the root into its prime factors, and then pair the factors. Each pair can be taken out of the root as a single number.

Front

What is the process for adding or subtracting radicals?

Back

To add or subtract radicals, they must have the same index and radicand. If they do, combine the coefficients of the radicals. If not, simplify them first if possible.

Front

What does it mean to simplify a radical expression?

Back

Simplifying a radical expression means rewriting it in its simplest form, which often involves reducing the radicand and removing any perfect squares or cubes.

Front

What is the cube root of a number?

Back

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is denoted as ∛x.

Front

How do you subtract radicals with different radicands?

Back

You cannot directly subtract radicals with different radicands. You must simplify them first or express them in a common form if possible.

Front

What is the value of √(a^2)?

Back

The value of √(a^2) is |a|, which means the absolute value of a.

Front

How do you combine like terms in radical expressions?

Back

Like terms in radical expressions can be combined if they have the same index and radicand. For example, 3√2 and 5√2 can be combined to make 8√2.

Front

What is the difference between a square root and a cube root?

Back

A square root (√) is a number that, when multiplied by itself, gives the original number, while a cube root (∛) is a number that, when multiplied by itself three times, gives the original number.

Front

What is the simplified form of √(18)?

Back

The simplified form of √(18) is 3√2, since 18 = 9 * 2 and √9 = 3.