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- Find the square root of a number.
- Estimate square roots.
- Simplify square roots that are not a perfect square.
- Simplify expressions that contain square roots.
- Identify radicands and radical expressions.
- Evaluate the square roots of perfect squares.
- Factor radical expressions.
- Learn how to simplify radical expressions that have radicands as powers.
- Multiply and simplify radical expressions.
- Divide radical expressions.
- Simplify the square roots of quotients.
- Rationalize the denominators of radical expressions.
- Add and subtract using radical notation.
- Multiply radical expressions that contain two or more terms.
- Describe the steps involved in solving radical equations.
- Solve radical equations that include two radical terms.
1. How to Find the Square Root of a Number
Calculating the square root of a number is the inverse operation of squaring that number. Explore how to find square roots, the square of numbers, perfect and imperfect squares, and some square root practice examples.
2. Estimating Square Roots
Estimating square roots can be challenging, but it is one of the most common math operations. In this lesson, look at square roots, perfect square roots, the square roots of an imperfect square, estimating the square root, and example problems of all of these definitions.
3. Simplifying Square Roots When not a Perfect Square
When numbers are not perfect squares, their square roots can be challenging, however, it is possible to simplify square roots to make the square roots easier to see and use. Dive into ways the rules of mathematics are used to define perfect and imperfect squares and learn how to evaluate the square root of an imperfect square.
4. Simplifying Expressions Containing Square Roots
In mathematics, an expression contains at least two numbers connected by at least one operation, and those expressions containing square roots can be simplified. Learn about the definition of expressions, the language of radicals, and discover the steps needed for simplifying expressions containing square roots.
5. Radicands and Radical Expressions
Radical expressions refer to expressions that include radicals, or square root signs. Explore the definition of a radical symbol and radicand, and understand the rules for radical expressions, including why they only work with real numbers.
6. Evaluating Square Roots of Perfect Squares
A Perfect Square is found when a number is the square of another integer. Learn the notation of radicals in the language of math, and how to calculate the square-roots of Perfect Squares.
7. Factoring Radical Expressions
Radical expressions can be factored by following the product rule for radicals. Learn about radical expressions, how to identify and factor them, and how to apply the product rule to simplify a radical expression.
8. Simplifying Square Roots of Powers in Radical Expressions
Radical expressions are used to represent numbers that can be reduced to their base number based on their exponent. Learn about the description of a radical symbol, radical expressions with exponents, and how to simplify radical expressions.
9. Multiplying then Simplifying Radical Expressions
The terms under radical symbols with the same index can be combined through multiplication, then simplified. Learn how to multiply and simplify radical expressions by using the product rule, and review the examples.
10. Dividing Radical Expressions
Dividing of radical expressions is possible through using the quotient rule. Discover more about dividing radical expressions, including simplification of expressions and rationalization of the denominator.
11. Simplify Square Roots of Quotients
The quotient rule can be used to solve radical expressions. This lesson explores this idea and provides examples demonstrating how to simplify the square roots of quotients.
12. Rationalizing Denominators in Radical Expressions
Rationalizing denominators is a process that is used to simplify radical expressions as much as possible. Discover when a radical expression is finished, and learn how to rationalize a denominator with one term or more than one term.
13. Addition and Subtraction Using Radical Notation
In mathematics, a radical notation indicates the square root of a number. Learn how to do addition and subtraction using radical notation, and recognize that mathematics and algebra include terms that may not be like others though radicals are regarded as like terms.
14. Multiplying Radical Expressions with Two or More Terms
Multiplying radical expressions with two or more terms involves using the distributive property. Learn about multiplying radical expressions, the distributive property, and multiplying two binomials.
15. Solving Radical Equations: Steps and Examples
A radical equation is an equation in which a variable is under a radical. Learn to identify radicals, perform inverse operations, and solve radical equations through real-world examples.
16. Solving Radical Equations with Two Radical Terms
An equation containing a square root symbol, or radical, is called a radical equation. To solve a radical equation, you isolate the radical by squaring it. Learn the step-by-step process on how to solve radical equations with two radical terms by using the FOIL method and checking your work.
17. Finding the Square Root of 169
A square root of a number is a smaller number that can be multiplied by itself to result in the original number. Follow the steps of the example to learn how to find the square root of 169.
18. Finding the Cube Root of 216
A cube root of a number is simply another number that can be multiplied by itself three times to result in the given number. Learn how to find the cube root of 216 using the steps in the provided example.
19. Finding Square Root of Negative 1
Is it possible to take the square root of a negative number? What is the square root of negative 1? This lesson goes over the history and current uses of this concept.
20. Taking the Square Root of Negative 4
This lesson shows a step by step process for taking the square root of a negative number. We'll use the example of taking the square root of negative 4 to show you this process.
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Other chapters within the High School Algebra II: Tutoring Solution course
- Algebra II - Basic Arithmetic Review: Tutoring Solution
- Algebra II - Algebraic Expressions and Equations Review: Tutoring Solution
- Algebra II - Real Numbers: Tutoring Solution
- Algebra II - Complex and Imaginary Numbers Review: Tutoring Solution
- Algebra II - Exponents and Exponential Expressions Review: Tutoring Solution
- Algebra II - Properties of Functions Review: Tutoring Solution
- Algebra II - Linear Equations Review: Tutoring Solution
- Algebra II - Systems of Linear Equations: Tutoring Solution
- Algebra II - Inequalities Review: Tutoring Solution
- Algebra II - Matrices and Determinants: Tutoring Solution
- Algebra II - Absolute Value Review: Tutoring Solution
- Algebra II - Polynomials: Tutoring Solution
- Algebra II - Factoring: Tutoring Solution
- Algebra II - Graphing and Factoring Quadratic Equations Review: Tutoring Solution
- Algebra II - Rational Expressions: Tutoring Solution
- Algebra II - Graphing and Functions: Tutoring Solution
- Algebra II - Quadratic Equations: Tutoring Solution
- Algebra II - Exponential and Logarithmic Functions: Tutoring Solution
- Algebra II - Conic Sections: Tutoring Solution
- Algebra II - Sequences and Series: Tutoring Solution
- Algebra II - Sets: Tutoring Solution
- Algebra II - Combinatorics: Tutoring Solution
- Algebra II - Calculations, Ratios, Percent & Proportions Review: Tutoring Solution
- Algebra II - Statistics: Tutoring Solution
- Algebra II - Trigonometry: Tutoring Solution