Okay... so like here's the thing... I compleatly forgot how to do this and I don't know why... (probably because I'm stupid...) and the notes I took make no sense... all I know is what ever my teacher did, it was something a bit more complecated... I think, sorry for being ( enter choice of word. e.x. Stupid, dumb, ect.)

Question: √144 how do I rewrite the radical while extracting all the perfect sqares.

The number itself is a perfect square, so it's going to be hard to do. What I'm trying to say is that there won't be anything left over underneath the square root sign.

Perfect squares.

144: 4 * 36

√144 = √(4 * 36)

√144 - √4*√36

√144 = 2 * 6 = 12.

In my opinion, the better way to do it is to factor the number down to it's primes. This works much better with larger numbers.

Suppose you want √480

480: 2 * 240

480: 2 * 2 * 120

480: 2 * 2 * 2 * 60

480: 2 * 2 * 2 * 2 * 30

480: 2 * 2 * 2 * 2 * 2 * 15

480: 2 * 2 * 2 * 2 * 2 * 3 * 5

How do you know when to quit? There are 2 rules.

Keep dividing by a prime until it gives you a decimal remainder.
Keep dividing by the next prime until you have nothing but primes.

So now we have

√480 = √(2 * 2 * 2 * 2 * 2 * 3 * 5)

Here's your last rule: for every pair of like factors you take out one from underneath the root and throw the other one away.

√480 = 2 * 2√ 2 * 3 * 5

√480 = 4√30