# How do you simplify square roots? (examples of problems I need help with down below in the description)

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Simplify,

1) #sqrt(20)#

2) #12/sqrt(3)#

3) #sqrt(6)/12#

Simplify,

1)

2)

3)

See explanations below:

For instance

Here, the simplification is to factor the term inside the radical into two terms, one of which is a square and the other of which is not: You reduce the term inside the radical to the smallest number that can be achieved by applying this rule.

Example Two

Example Three

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To simplify square roots, follow these steps:

- Find the prime factorization of the number inside the square root.
- Identify pairs of the same factors.
- Take one factor from each pair outside the square root.
- Multiply the factors taken out to get the simplified square root.

Example 1: √48 = √(2^4 * 3) = 2^2 * √3 = 4√3

Example 2: √75 = √(3^1 * 5^2) = 5√3

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