Heres a neat little math tip: when you square root a number, you are essentially cancelling out half of that numbers prime factors.
What do we mean by that? Take a look at the square root of 36. Of course, the answer is 6, but lets break it down and go behind the scenes.
The prime factors of 36 are 2 x 2 x 3 x 3. So what you really have is:
SEE ILLUSTRATION 1
As we said, when you square root a number, you essentially are cancelling out half of each of the distinct primes. In this case, you cut out one 2 and one 3, leaving behind 2 x 3, or 6.
Now, to be clear, we are talking about half of each of the distinct prime factors. Take a look at the square root of 144. The prime factors of 144 are 2 x 2 x 2 x 2 x 3 x 3. There are four 2s and two 3s, so cancel out two 2s and one 3. You are left with 2 x 2 x 3, or 12.
Now you can square root numbers with ease. Whats the square root of 441? Just break it into primes: 3 x 3 x 7 x 7. Cut out a 3 and a 7, youre left with 21. What is the square root of 784? Primes are 2 x 2 x 2 x 2 x 7 x7, so the answer is 2 x 2 x 7, or 28.
In general, prime numbers are a great tool to utilize when dealing with number properties questions on the GMAT. Stay tuned
well cover other ways in future posts.


