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 ∛x.

Tags

CCSS.8.NS.A.1

Front

How do you simplify the expression √a * √b?

Back

You can simplify √a * √b to √(a*b).

Front

What is the product of two square roots, √a and √b?

Back

The product is √(a*b).

Front

How do you simplify the expression (a√b)(c√d)?

Back

You can simplify it to ac√(b*d).

Tags

CCSS.HSN.RN.A.2

Front

What is the sum of two like radical expressions, such as 3√5 + 2√5?

Back

The sum is 5√5, as you can combine the coefficients.

Front

How do you subtract radical expressions, for example, 5√2 - 3√2?

Back

You subtract the coefficients: (5 - 3)√2 = 2√2.

Front

What is the result of simplifying -3√17 - 4√17?

Back

The result is -7√17, as you combine the coefficients.

Front

How do you multiply radical expressions, such as (2√2)(3√10)?

Back

You multiply the coefficients and the radicands: (2*3)√(2*10) = 6√20 = 12√5 after simplification.

Front

What is the cube root of a number?

Back

The cube root of a number x is a value y such that y^3 = x.

Tags

CCSS.8.EE.A.2

Front

How do you simplify the expression √(a^2)?

Back

The simplification is |a|, as the square root of a squared value is the absolute value of that number.