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Math 71B

7.3 – Multiplying and Simplifying Radical Expressions

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(Disclaimer: Only works when are real #s. Some restrictions apply. See stores for details.)

Product Rule for Radicals

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Ex 1.Multiply:

Product Rule for Radicals

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Ex 1.Multiply:

Product Rule for Radicals

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Ex 1.Multiply:

Product Rule for Radicals

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4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, …are ___________________ (squares of integers)

8, 27, 64, 125, 216, 343, … are ______________

16, 81, 256, 625, … are ____________________

Simplifying Radicals

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4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, …are ___________________ (squares of integers)

8, 27, 64, 125, 216, 343, … are ______________

16, 81, 256, 625, … are ____________________

Simplifying Radicals

perfect squares

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4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, …are ___________________ (squares of integers)

8, 27, 64, 125, 216, 343, … are ______________

16, 81, 256, 625, … are ____________________

Simplifying Radicals

perfect squares

perfect cubes

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4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, …are ___________________ (squares of integers)

8, 27, 64, 125, 216, 343, … are ______________

16, 81, 256, 625, … are ____________________

Simplifying Radicals

perfect squares

perfect cubes

perfect fourth powers

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Ex 2.Simplify:

Simplifying Radicals

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Recall: If is even, . If is odd, .

Note: If is nonnegative, then the first rule becomes _____.

Simplifying Radicals

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Recall: If is even, . If is odd, .

Note: If is nonnegative, then the first rule becomes _____.

Simplifying Radicals

𝒂

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Ex 3.Simplify (assume that all variables are positive real numbers).

Simplifying Radicals

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Ex 4.Multiply and simplify (assume that all variables are positive real numbers):

Simplifying Radicals