Adding and Subtracting Radicals

Front

What is a radical?

Back

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

Tags

CCSS.8.NS.A.1

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|.