Simplifying Radical Expressions – Practice Problems

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For a radical expression to be in the simplest form, three conditions must be met:
1. The radicand contains no factor greater than 1 that is a perfect square.
2. There is no fraction under the radical sign.
3. There is no radical in the denominator of a fraction. The procedure used to remove a radical from a denominator is called rationalizing the denominator.

A knowledge of perfect squares and the product property of square roots can be very helpful in simplifying radical expressions. The property states that the root of the product of two terms is equal to the product of the root of each term.

To use the product property of square roots to simplify a radical expression, first write the radicand as the product of a perfect square and a factor that does not contain a perfect square. Then use the product property of square roots to write the expression as a product. Finally, simplify the radical expression.

Another useful property for simplifying radical expressions is the quotient property of square roots; it is used to divide radical expressions. The property states that the root of a rational number is equal to the root of the numerator divided by the root of the denominator.

In a similar fashion, the quotient property can be used to simplify a radical expression by first writing the expression as the root of the numerator divided by the root of the denominator, then simplifying the root in the numerator and the root in the denominator, and finally simplifying the resulting radical.

Expressions and Equations Work with radicals and integer exponents.

CCSS.MATH.CONTENT.8.EE.A.2

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Exercises in this Practice Problem
Determine the distance $c$.
Explain how to multiply and divide radical expressions.
Decide which radical expressions can be simplified.
Determine the missing length.
Label the parts of a radical expression.
Simplify the radical expressions.