Add and Subtract Radicals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the operation of finding a number that, when multiplied by itself a certain number of times, gives the original number.

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, and then take out pairs of factors for square roots (or appropriate groups for higher roots). For example, √18 = √(9*2) = 3√2.

Front

What does it mean to add radicals?

Back

To add radicals, you can only combine them if they have the same index and radicand. For example, √2 + √2 = 2√2, but √2 + √3 cannot be simplified further.

Front

What is the process for subtracting radicals?

Back

Subtracting radicals follows the same rules as adding them. You can only subtract radicals with the same index and radicand. For example, 3√5 - 2√5 = (3-2)√5 = 1√5.

Front

What is the index of a radical?

Back

The index of a radical indicates the degree of the root being taken. For example, in the square root √x, the index is 2 (implied), and in the cube root ∛x, the index is 3.

Front

Can you add or subtract different radicals?

Back

No, you cannot add or subtract different radicals (e.g., √2 + √3) because they do not have the same radicand. They remain separate terms.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Front

How do you rationalize the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by a radical that will eliminate the radical in the denominator. For example, to rationalize 1/√2, multiply by √2/√2 to get √2/2.

Front

What is the difference between like and unlike radicals?

Back

Like radicals have the same radicand and index (e.g., 2√3 and 5√3), while unlike radicals have different radicands or indices (e.g., √2 and √3).

Front

What is the result of (√5 + √5)?

Back

The result is 2√5, as you can combine like radicals.