Add, Subtract, and Multiply Radicals

Front

What is a radical?

Back

A radical is a symbol that represents the root of a number, most commonly the square root. For example, √4 represents the square root of 4, which is 2.

Front

How do you simplify √a * √b?

Back

√a * √b = √(a * b). For example, √2 * √3 = √(2 * 3) = √6.

Front

What is the process to add radicals?

Back

To add radicals, they must have the same index and radicand. For example, √2 + √2 = 2√2, but √2 + √3 cannot be simplified further.

Front

How do you subtract radicals?

Back

Similar to addition, you can only subtract radicals with the same index and radicand. For example, 3√5 - 2√5 = (3-2)√5 = 1√5.

Front

What is the square root of 20?

Back

√20 can be simplified to 2√5, since 20 = 4 * 5 and √4 = 2.

Front

How do you multiply a radical by a whole number?

Back

To multiply a radical by a whole number, simply multiply the whole number by the coefficient of the radical. For example, 3 * √2 = 3√2.

Front

What is the result of √a + √a?

Back

√a + √a = 2√a, since you are adding like terms.

Front

How do you simplify the expression -3√20 - √5?

Back

-3√20 - √5 = -3(2√5) - √5 = -6√5 - √5 = -7√5.

Front

What is the result of 3√8 + 3√2?

Back

3√8 + 3√2 = 3(2√2) + 3√2 = 6√2 + 3√2 = 9√2.

Front

How do you simplify -2√2 - 3√8 - √5?

Back

-2√2 - 3√8 - √5 = -2√2 - 3(2√2) - √5 = -2√2 - 6√2 - √5 = -8√2 - √5.