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 simplify √a + √b?

Back

You can only add √a and √b if they have the same radicand (the number under the root). If they do, combine them as coefficients.

Front

What is the simplified form of √300?

Back

√300 = √(100 * 3) = 10√3.

Front

What is the simplified form of √75?

Back

√75 = √(25 * 3) = 5√3.

Front

How do you add √12 and √192?

Back

First, simplify both: √12 = 2√3 and √192 = 8√3. Then, add: 2√3 + 8√3 = 10√3.

Front

What is the result of 4√7 - 10√7 + 7√7?

Back

Combine like terms: (4 - 10 + 7)√7 = 1√7 = √7.

Front

What is the sum of (3√6) + (4√6)?

Back

Combine like terms: (3 + 4)√6 = 7√6.

Front

How do you simplify -2√2 - 3√8 - √5?

Back

First, simplify √8 = 2√2. Then, combine: -2√2 - 6√2 - √5 = -8√2 - √5.

Front

What is the principle of combining radicals?

Back

You can combine radicals only if they have the same radicand.

Front

What is the difference between adding and subtracting radicals?

Back

Adding radicals combines their coefficients, while subtracting involves subtracting the coefficients.