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Simplifying Radicals Study Guide (page 4)

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Updated on Aug 24, 2011

Multiplying and Dividing Radicals

To multiply radicals like 4√3 by 2√2, you multiply the numbers in front of the radicals: 4 times 2. Then multiply the radicands: 3 times 2. The answer is 8√6.

Example: 5√3 · 2√2

Multiply the numbers in front of the radicals. Then multiply the radicands.

10√6

Example: 2√6 · 3√3

Multiply the numbers in front of the radicals. Then multiply the radicands.

6√18

However, you are not finished yet because 18 contains the factor 9, which is a perfect square.

6√2 · 9

Take out the square root of 9.

3 · 6√2

Simplify.

18√2

Tip

When you multiply or divide radicals, the radicands do not have to be the same.

To divide the radical 4√6 by 2√3, divide the numbers in front of the radicals. Then divide the radicands.The answer is 2√2.

Example:

Divide the numbers in front of the radical. Then divide the radicands.

2√3

Example:

Divide the numbers in front of the radicals. Then divide the radicands.

2√4

However, you aren't finished yet because 4 is a perfect square.

Take the square root of 4.

2 · 2

Simplify.  4

Tip

If there is no number in front of the radical sign, it is assumed to be 1.

Skill Building until Next Time

Think about the formula for the area of a rectangle: A = lw. Why do you use square when you multiply a number by itself? What word would you use when multiplying a number by itself three times? Why isn't there a commonly used word for multiplying a number by itself four times?

Find practice problems and solutions for these concepts at Simplifying Radicals Practice Problems.

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