Adding and Subtracting Radicals

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square 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, 2√5 + 4√5 = (2+4)√5 = 6√5.

Front

What is the result of √a - √b when a = 18 and b = 8?

Back

The result is √18 - √8 = √(9*2) - √(4*2) = 3√2 - 2√2 = (3-2)√2 = √2.

Front

What is the simplified form of √25?

Back

The simplified form of √25 is 5.

Front

How do you subtract radicals?

Back

To subtract radicals, ensure they have the same index and radicand, then subtract their coefficients. For example, √a - √a = 0.

Front

What is the sum of (5√3) + (6√3)?

Back

The sum is 11√3.

Front

What is the simplified form of 2√5?

Back

2√5 is already in its simplest form.

Front

How do you simplify √(a*b)?

Back

You can simplify √(a*b) to √a * √b, provided a and b are non-negative.

Front

What is the result of (3√6) + (4√6)?

Back

The result is 7√6.

Front

What is the process to simplify √(a^2)?

Back

The process is to take the absolute value of a, so √(a^2) = |a|.