how do you simplify square roots?

Question

how do you simplify square roots?

i know you have to take factors out of the square root symble and all of that but not exactly.
please help

Answer 1

Let's say you have sqrt(144)....

You know, 12*12 is 144. That means sqrt(144) = sqrt(12*12) then it will simplify to simply 12.

Now, lets say you have sqrt(288).

From above, you know, sqrt(144) is sqrt(12*12). You also know, sqrt(288) is sqrt(12*12*2). That means, you can simplify it to 12*sqrt(2)

Now, let's say you have sqrt(432)...

From above, you know 432 is 12*12*3. That will simplify to 12*sqrt(3)

NOW, let's say you have sqrt(576)... You know it means sqrt(12*12*4) right? But you also know 2*2 is 4.

THAT means, it is 12*12*2*2.... also know as 24*24. Therefore, it will simiplify to just 24.

Do you see a pattern? A trick is, for you to know many numbers that are result of squaring something. Then you can start finding, how you can divide what is in the radical sign without having a remainder.

Answer 2

Question 1 √54 = √(9 x 6) = 3.√6 Question 2 √ (10/32) = √((2 x 5) / (2 x 16)) = [√(5/16) ] = (1/4).√5