Answer:
Step-by-step explanation:
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
