Simplify Radical Expression Worksheets

Printable “Radical Expressions” worksheets:
Simplify square roots
Rationalize denominators
Add & Subtract Radical Expressions
Multiply Radical Expressions
Divide Radical Expressions
Equivalent Rational Expressions

Examples, solutions, videos, and worksheets to help Algebra II students learn how to convert expressions to simplest radical form. Understand that the product of conjugate radicals can be viewed as the difference of two squares.

How to Simplify Radical Expressions?

Simplifying radicals involves rewriting the expression so that the radical has no perfect square (or cube, etc.) factors other than 1.

Simplifying Radicals

1. Factor the radicand:
   Find the largest perfect square factor of the radicand.
   
2. Apply the product rule:
   Separate the radical into two radicals, one for the perfect square and one for the remaining factor.
   
3. Simplify the perfect square root:
   Take the square root of the perfect square.

Example:
√75 = √(25 * 3)
= √25 * √3
= 5√3

Simplifying Using Conjugates

Sometimes, you can simplify a radical expression by multiplying by the conjugate.
The conjugate of a binomial expression is formed by changing the sign between the two terms.

Example:
The conjugate of 5 - √3 is 5 + √3.
(5 - √3) * (5 + √3) = (5² - (√3)²) = 22

Conjugates are often used to rationalize the denominator of a fraction involving radicals. This involves multiplying both the numerator and denominator by the conjugate of the denominator to eliminate the radical from the denominator.

Have a look at this video if you need to review how to Simplify Radical Expressions.

• Simplify Radical Expressions

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More Simplify Radical Expression Worksheets

Printable
(Answers on the second page.)
Simplify Radical Expression Worksheet #1
Simplify Radical Expression Worksheet #2
Simplify Radical Expression Worksheet #3

Related Lessons & Worksheets

Radicals & Conjugates
Simplify Radical Expressions
Simplify Radical Expressions with Fractions

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