Do you understand that
Hi All,
I'm new to the forum so firstly hello. The following question may be rudimentary given the level of ability of some of you but I would very much appreciate a clear understanding/answer.
1. Can someone help me understand how 2√27 simplifies to (2 X 3 X √3).
2. Can someone help me understand how 3^√27 X 3^√3 simplifies to 3^3√3
I've read quite a few of the web manuals on Powers and Roots but these specific examples are a block for me. If anyone can point me towards a comprensive resource I'd very much appreciate it.
Thanks in Advance.
Removed. figured it out. So just to post the solution...
1. Can someone help me understand how 2√27 simplifies to (2 X 3 X √3).
1a. Factor of 27 is 3 * 9. 9 is 3^2
1b. Simplifies to 2√3^2 X 2 = 2√3^2 * √3
1c. √3^2 = 3
1d. Leaving 2 * 3 * √3
2. Can someone help me understand how 3^√27 X 3^√3 simplifies to 3^3√3
2a. Factor of 27 is 3 * 9. 9 is 3^2
2b. Simplifies to 3 X √3 * 9
2c. Simplifies to 3 X √3 * √3^2
2d. Leaving 3 X 3 * √3
Thanks to all.
I would review how to get the prime factorization of a number using factor trees. For example, do you see why
Now, you can take the square root of 3000 as follows:
This is a systematic procedure that will always get you the answer. After you're comfortable with this you can begin to use shortcuts such as
Note that I know that can't be reduced further because the prime factorization of 30 has no exponents greater than 1.
Perhaps someone who is better at latex than me can draw a factor tree for 3000?