Mathematics
Grade 11
15 min
Add and subtract radical expressions
Add and subtract radical expressions
What you'll learn
- Solve one-step word problems involving addition and subtraction with numbers up to 100, showing your work, with 80% accuracy.
- Identify whether a word problem requires addition, subtraction, multiplication, or division, and explain why you chose that operation.
- Apply multiplication and division strategies (like drawing pictures or using repeated addition/subtraction) to solve one-step word problems with numbers up to 50, with 70% accuracy.
- Explain in your own words how addition and multiplication are related, using examples from word problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify like and unlike radical terms based on their index and radicand.
Simplify radical expressions by factoring out perfect squares, cubes, or other nth powers.
Combine like radical terms by adding or subtracting their coefficients.
Add and subtract expressions containing multiple radical terms, some of which require simplification first.
Simplify and combine radical expressions that include variables in the radicand.
Apply the distributive property to multiply a monomial by a binomial containing radicals.
You know that 3x + 5x = 8x, but what about 3√2 + 5√2? 🤔 It works almost exactly the same way!
This tutorial will teach you how to add and subtract radical expressions. You'll learn that this process is very similar to combining like terms in...
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Key Concepts & Vocabulary
TermDefinitionExample
Radical ExpressionAn expression that contains a root (square root, cube root, etc.). The symbol for the root is called the radical sign (√).5√3, √x, and 2∛(7y) are all radical expressions.
RadicandThe number or expression found inside the radical sign.In the expression √18, the radicand is 18.
IndexThe small number to the left of the radical sign that indicates which root is being taken.In the expression ∛8, the index is 3. If no index is written, it is assumed to be 2 (a square root).
Like RadicalsRadical terms that have the exact same index and the exact same radicand.7√5 and -2√5 are like radicals. However, 7√5 and 7∛5 are not (different indices).
Simplest Radical FormA radical is in its simplest form when the radicand contains no perfect square factors (or perfec...
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Core Formulas
Combining Like Radicals
a√[n]{x} + b√[n]{x} = (a + b)√[n]{x}
To add or subtract like radicals, you add or subtract their coefficients (the numbers in front of the radical) and keep the radical part the same. This is analogous to combining like terms such as 2x + 3x = 5x.
Product Rule for Radicals
√[n]{ab} = √[n]{a} * √[n]{b}
This rule is essential for simplifying radicals. It allows you to break down a radicand into its factors and separate them into different radicals, which helps in finding and extracting perfect nth powers.
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Challenging
Expand and simplify the expression: (2√3 - √6)(√3 + 4√6)
A.6 + 7√18 - 24
B.-18 + 21√2
C.30 + 7√18
D.-18 - 7√2
Challenging
Simplify the expression, assuming a, b ≥ 0: √(72a³b⁴) - a√(18ab⁴)
A.3ab²√2a
B.9ab²√a
C.0
D.3ab²√a
Challenging
Which of the following expressions is equivalent to 2√108 - 3√48 + √3?
A.0
B.2√63
C.-√3
D.√3
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Frequently asked questions
What grade level is "Add and subtract radical expressions"?
Add and subtract radical expressions is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract radical expressions?
You'll be able to: Solve one-step word problems involving addition and subtraction with numbers up to 100, showing your work, with 80% accuracy; Identify whether a word problem requires addition, subtraction, multiplication, or division, and….
Is "Add and subtract radical expressions" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Add and subtract radical expressions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.