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Algebra 1

Simplifying Radicals: Mini-Lesson Review

Algebra 1Simplifying Radicals: Mini-Lesson Review

Simplifying Radicals: Mini-Lesson Review

Simplifying Radicals: Mini-Lesson Review

Mini Lesson Question

Question #1: Simplifying Radicals

Simplify 45 .
  1. 5 9
  2. 9 5
  3. 5 3
  4. 3 5

Simplifying a Square Root

Some square roots can be simplified using the product property. Here is the product property:

Product Property of n t h n t h Roots

If a n a n and b n b n are real numbers, and n ≥ 2 n ≥ 2 is an integer, then

a b n = a n · b n a b n = a n · b n and a n · b n = a b n a n · b n = a b n

Here is how the product property can be used to simplify square roots:

How to Simplify a Radical Expression Using the Product Property

Step 1 - Find the largest factor in the radicand that is a perfect power of the index. Use that factor to rewrite the radicand as a product of two factors.

Step 2 - Use the product rule to rewrite the radical as the product of two radicals.

Step 3 - Simplify the root of the perfect power.

Example

Find the simplest form of 98 98 .

Step 1 - Find the largest factor in the radicand that is a perfect power of the index. Use that factor to rewrite the radicand as a product of two factors. We see that 49 is the largest factor of 98 that has a power of 2. In other words, 49 is the largest perfect square factor of 98.

98 = 49 · 2 98 = 49 · 2 Always write the perfect square factor first. 49 · 2 49 · 2

Step 2 - Use the product rule to rewrite the radical as the product of two radicals.

49 · 2 49 · 2

Step 3 - Simplify the root of the perfect power.

7 2 7 2

Try it

Simplifying a Square Root

Simplify 48 48 .

Check Your Understanding

Find the simplest form of 500 500 .

  1. 10 5 10 5

  2. 100 5 100 5

  3. 5 20 5 20

  4. 2 125 2 125

Video: Simplifying Square Roots Using Perfect Squares

Watch the following video to learn more about how to simplify square roots using perfect squares.

Khan Academy: Simplifying Square Roots

Simplifying square roots | Exponents, radicals, and scientific notation | Pre-Algebra | Khan Academy

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