Examples

Using previous knowledge of
Perfect Squares

Step 1
Consider the factors of 20 (and recall the principal square roots and perfect squares tables you built in Coach's Corner - I).

Step 2
Identify the set of factors where one factor is a perfect square greater than 1.

Step 3
Express 20 as a product of its factors.

Step 4
Separate and give each factor its own radical sign.

Step 5
The so rewrite as a simplified mixed radical.

Using previous knowledge of Prime Factorization Trees

Step 1
Using a prime factorization tree, find the prime factors of 20.

Step 2
The index for is 2 because it is a square root. As such, identify the prime factors of 20 that repeat (doubles).

Step 3
Rewrite the radical as a product of its prime factors.

Step 4
Rewrite as a simplified mixed radical.

Using previous knowledge of
Perfect Squares

Step 1
Consider the factors of 226 (and recall the principal square roots and perfect squares tables you built in Coach's Corner - I).

Step 2
Identify the set of factors where one factor is a perfect square greater than 1.

For 226, there is no such set of factors. As such, the radical cannot be further simplified.

Using previous knowledge of Prime Factorization Trees

Step 1
Using a prime factorization tree, find the prime factors of 226.

Step 2
Identify the prime factors of 226 that repeat (doubles).

There are no prime factors of 226 that repeat. As such, the radical cannot be further simplified.