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

Simplify,
1) #sqrt(20)#

2) #12/sqrt(3)#

3) #sqrt(6)/12#

Question

Simplify,
1) #sqrt(20)#

2) #12/sqrt(3)#

3) #sqrt(6)/12#

Genesis Allen · Accepted Answer

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. #sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))# #sqrt(20) => sqrt(color(red)(4) * color(blue)(5)) => sqrt(color(red)(4)) * sqrt(color(blue)(5)) => 2sqrt(5)# Example Two The simplification in this example is to rationalize the denominator. Or in other words, to remove all radicals from the denominator. You do this by multiplying by the appropriate form of #1#" #12/sqrt(3) => sqrt(3)/sqrt(3) xx 12/sqrt(3) => (12sqrt(3))/(sqrt(3))^2 => (12sqrt(3))/3 => 4sqrt(3)# Example Three This is in simplified radical form. There denominator is rationalize - there is no radical in the denominator. The #sqrt(6)# cannot be simplified as in Example 1. We can put this into exponent form using this rule: #root(color(red)(n))(x) = x^(1/color(red)(n))# #sqrt(6)/12 => root(2)(6)/(2 * 6) => 6^(1/2)/(2 * 6^1) => 1/(2 * 6^(1-1/2)) => 1/(2 * 6^(1/2))#

Jace Anderson · Answer

undefined To simplify square roots, follow these steps:
1. Find the prime factorization of the number inside the square root.
2. Identify pairs of the same factors.
3. Take one factor from each pair outside the square root.
4. 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

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

Simplify, 1) #sqrt(20)# 2) #12/sqrt(3)# 3) #sqrt(6)/12#

Simplify,
1) #sqrt(20)#

2) #12/sqrt(3)#

3) #sqrt(6)/12#