Adding and Subtracting Radicals

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

How do you simplify √18?

Back

√18 can be simplified to 3√2 because 18 = 9 * 2 and √9 = 3.

Front

What is the process of adding radicals with the same index?

Back

To add radicals with the same index, combine the coefficients (numbers in front) of the radicals while keeping the radical part the same.

Front

What is the process of subtracting radicals with the same index?

Back

To subtract radicals with the same index, subtract the coefficients of the radicals while keeping the radical part the same.

Front

Simplify: √8 - √18

Back

√8 - √18 = 2√2 - 3√2 = -√2.

Front

What is the result of (3√6) + (4√6)?

Back

The result is 7√6 because you add the coefficients: 3 + 4 = 7.

Front

What is the result of (5√7) - (11√7)?

Back

The result is -6√7 because you subtract the coefficients: 5 - 11 = -6.

Front

How do you combine like radicals?

Back

Combine like radicals by adding or subtracting their coefficients if they have the same radical part.

Front

What is the simplified form of 4√7 - 10√7 + 7√7?

Back

The simplified form is √7 because 4 - 10 + 7 = 1.

Front

What is √a - √b?

Back

It cannot be simplified further unless a and b are perfect squares or can be combined.