Simplifying Radicals

1
Simplifying Radicals

• Algebra 1 Section 9.2

2
Simplifying the Square Root of a Product

• If the number under the radicand is a product,
  you can simplify the square root into the product
  of the square roots.
• In symbols .
• Example
• Example
• Example
• Example

3
Perfect Square Factors

• A perfect square factor is a factor of a number
  which is also a perfect square.
• For example 20 4 5.
• Since 4 is a perfect square (22), 4 is a perfect
  square factor of 20.
• We use this technique to simplify square roots.
• For example

4
Perfect Square Factors

1. Simplify
2. Solution
3. Simplify
4. Solution
5. Simplify
6. Solution

5
Simplifying the Square Root of a Quotient

1. If the number under the radicand is a fraction,
   you can simplify the square root into the
   quotient of the square roots.
2. In symbols
3. Example
4. Example

6
Rationalizing the Denominator

1. When you find the square root of a quotient,
   there is often a square root in both the
   numerator and denominator.
2. For the purposes of operations with fractions, it
   is often beneficial to rationalize the
   denominator.
3. To rationalize the denominator, multiply both the
   numerator and denominator by the denominator.
4. This will square the radicand in the denominator,
   thus removing it.

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Rationalizing the Denominator

1. Rationalize
2. Solution
3. Rationalize
4. Solution