Check: Operations with Radical Expressions

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, √x or ∛y.

Front

How do you simplify √a * √b?

Back

√a * √b = √(a * b). For example, √3 * √4 = √(3 * 4) = √12.

Front

What is the process to simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, then simplify by taking out pairs of factors.

Front

Simplify: 6√3 + 2√75 - 4√27

Back

4√3.

Front

What is the value of √(a^2)?

Back

The value of √(a^2) is |a|, which means the absolute value of a.

Front

How do you combine like terms in radical expressions?

Back

You can combine like terms in radical expressions if they have the same radical part. For example, 3√2 + 5√2 = 8√2.

Front

Simplify: √28 * √3

Back

2√21.

Front

What is the rule for multiplying radicals?

Back

The rule for multiplying radicals states that √a * √b = √(a * b).

Front

Simplify: -2√2 - 3√8 - √5

Back

-8√2 - √5.

Front

What is the value of √(x^2 + y^2) when x = 3 and y = 4?

Back

√(3^2 + 4^2) = √(9 + 16) = √25 = 5.