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Bell Quiz
Objectives
• Simplify basic square root expressions
Square Roots
• A number has both a positive and negative square root.
• The principal square root is the positive square root of a number.
• Typically, if no negative sing is present, the principal square root is calculated.
Example 1Simplifying Expressions Using the Positive and Negative
Values of the Square Root
Simplify the expression
Lesson Practice 1
Simplify the expression
Example 2Simplifying Expressions Using the Positive and Negative
Values of the Square Root
Simplify the expression
Lesson Practice 2
Simplify the expression
Example 3Simplifying Expressions Using the Positive and Negative
Values of the Square Root
Simplify the expression
Lesson Practice 3
Simplify the expression
Example 4Simplifying Expressions Using the Positive and Negative
Values of the Square Root
Simplify the expression
Lesson Practice 4
Simplify the expression
Example 5Simplifying Expressions Using the Positive and Negative
Values of the Square Root
Simplify the expression
Lesson Practice 5
Simplify the expression
Higher – Order Roots
• Higher order roots can be calculated in a similar way that square roots are calculated.
• The cube root is a number, written as , whose cube is x.
• For example, the cube root of 8 is 2 because 23 = 8.
• The cube root of 8 is writing as .
Example 6Simplifying Roots
Simplify the expression
Lesson Practice 6
Simplify the expression
Example 7Simplifying Roots
Simplify the expression
Lesson Practice 7
Simplify the expression
Example 8Simplifying Roots
Simplify the expression
Lesson Practice 8
Simplify the expression
Example 9Simplifying Roots
Simplify the expression
Lesson Practice 9
Simplify the expression
Higher – Order Roots
• Roots can be written as fractional exponents.• Consider the expression ()2 – Using the Power of a Power Property, the
expression simplifies to .• This is equivalent to the statement ()2 = .
Example 10Simplifying Expressions With Fractional Exponents
Simplify the expression
Lesson Practice 10
Simplify the expression
Example 11Simplifying Expressions With Fractional Exponents
Simplify the expression
Lesson Practice 11
Simplify the expression
Example 12Simplifying Expressions With Fractional Exponents
Simplify the expression
Lesson Practice 12
Simplify the expression
Example 13Simplifying Expressions With Fractional Exponents
Simplify the expression
Lesson Practice 13
Simplify the expression
Example 14Application: Volume
A gift box in the shape of a cube has a volume of 3375 cubic inches. What is the side length of the box?
Lesson Practice 14
A sculpture in the shape of a cube has a volume of 1728 cubic feet. What is the side length of the block?
