Adding and Subtracting 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 (∛).

Front

How do you add radicals with the same index and radicand?

Back

You can add radicals with the same index and radicand by adding their coefficients. For example, 3√6 + 4√6 = (3+4)√6 = 7√6.

Front

What is the process for subtracting radicals?

Back

To subtract radicals, ensure they have the same index and radicand, then subtract their coefficients. For example, 5√7 - 11√7 = (5-11)√7 = -6√7.

Front

What does it mean to simplify a radical expression?

Back

Simplifying a radical expression means to reduce it to its simplest form, which often involves factoring out perfect squares or cubes.

Front

How do you simplify √18?

Back

√18 can be simplified to √(9*2) = √9 * √2 = 3√2.

Front

What is the result of (3√2) - (3√18)?

Back

The result is -6√2 after simplifying 3√18 to 9√2.

Front

What is the result of (6√2) - (4√18)?

Back

The result is -6√2 after simplifying 4√18 to 12√2.

Front

What is the sum of (3√6) + (4√6)?

Back

The sum is 7√6.

Front

What is the difference of (13√13) - (6√13)?

Back

The difference is 7√13.

Front

How do you combine like radicals?

Back

Combine like radicals by adding or subtracting their coefficients while keeping the radical part unchanged.