Simplifying square roots (or radicals)

We will look into two methods that can be used to simplify square roots (or radicals): the perfect square method and the prime factorization method.

Simplify square roots using the perfect square method

The steps involved are:

1. Find the perfect square(s) that will divide the number in the square root.

2. Write the number as a factor of the perfect square(s).

3. Reduce the perfect squares.

Example:

Simplify

Solution:

Step 1: The perfect square 16 divides 48

Step 2: Write 48 as a factor of 16

48 = 16 × 3

Step 3: Reduce square root of 16

The following video shows more examples of simplifying square roots using the perfect square method.

Simplify square roots using the prime factorization method

The steps involved are:

1. Break the number in the square root into prime factors

2. For each pair of factors, “take one out” of the square root sign

3. The remaining factors in the square root sign are multiplied together.

Example:

Simplify

Solution:

Step 1. Break the number 12 into prime factors

12 = 2 × 2 × 3

Step 2: Take 2 out of the square root sign

Example:

Simplify

Solution:

Step 1. Break the number 90 into prime factors

90 = 2 × 3 × 3 × 5

Step 2: Take 3 out of the square root sign

Step 3: Multiply 2 and 5

The following video shows more examples of simplifying square roots using the prime factorization method.

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