How Do You Simplify Radicals Using the Product Property?

The symbol above the 60 is a square root sign
Writing out the prime factorization of 60 makes it easier to simplify the radical
A prime number is a number whose only factors are 1 and itself
Break up the problem into multiple radicals to make it easier to simplify
Squaring and taking the square root are opposite operations, so they cancel each other out

1. Writing out the prime factorization of 60 will make it easier to simplify the radical
1. A prime number is a number whose only factors are 1 and itself
2. 2•2•3•5 is the prime factorization of 60
1. Rewriting multiple factors using exponents makes it easier to see what can be taken out of the radical
1. This property lets us break up a radical into the product of multiple radicals
1. This property lets us break up a radical into the product of multiple radicals
2. So we can break √(2²•3•5) into √(2²)•√(3•5)
3. Breaking the radical up like this will make it easier to simplify
1. A perfect square can be written as something squared
2. Squaring and taking the square root are opposite operations
3. They cancel each other out!
4. Since neither 3 nor 5 are perfect squares, we can just multiply them back together to simplify
1. The number under the radical, 15, doesn't have any perfect square factors
2. That means our expression is in simplest form!

Write the √60 in its simplest form.