how do you simplify radicals

Question

I don't know the steps to  simplifying radicals. 

Answer 1

The first step is to determine if you can factor out a perfect square from the number inside of the radical. A perfect square is a number (such as 9) whose square root is a whole number (which would be 3). Then, find the root of the perfect square and multiply it with anything in front of your radical.

 

Step 1:

4√18

Factor √18 to √9 * √2 as 9 is a perfect square

 

Step 2:

4*√9*√2

4*3*√2

12√2

Answer 2

It would be much easier if you gave us an example but I'll try to illustrate.

 

First lets say we have sqrt(25) / sqrt(36)    where sqrt means square root

 

in this simple case, you should know that square root of 25 is 5 (since 25=5*5) and square root of 36 is 6 (since 36=6*6)

 

so the answer would be 5/6

 

now lets say we have sqrt (72) / sqrt (60)

 

first we can write this as just one square root:   sqrt(72/60)    now we can sow reduce the fraction 72/60 = 36/30 =18/15=6/5     (you could just divide top and bottom by 12)

 

so sqrt (72/60) = sqrt (6/5) and you can not simplify that.

 

In general you have to factor the numbers and have those number written in terms of powers of two. That is because numbers that are raised to power of two can come out of the square root.

 

for instance sqrt(20) = sqrt(2*2*5) = sqrt(2² *5) = 2*sqrt(5)

 

Please let me know if you have any specific question.