| By Yusuf Mohamed on Saturday, October 19, 2002 - 04:19 am: |
I have a big problem with radicals.
So what in the world is 7 sqrt 3 suppose to mean?
And how are the ways to put it back to normal?
Thanks alot!!
| By Marcos Charalambides on Saturday, October 19, 2002 - 06:14 am: |
Okay I'll try explain the general idea...
If you have the equation x2 = 4 (x is positive) the
solution is simply 2
But what if you had x2 = 2?
Using a calculator you get 1.41421... but this is only an
approximation so it is better if you just leave the answer as
sqrt 2. This is more concise and more accurate as you're not
rounding off anything...
Now,
Using the fact that (ab)n = an
bn and noting that p1/2 means the square
root of p we can do the following:
Say we had
We can write this as (12)1/2 =
(3x4)1/2
By the rule I mentioned before you can split this up...
Therefore,
(3x4)1/2 = (3)1/2 (4)1/2
But
and so
(or
, it's
more common to put the rational number first)
So we have...
(
basically just means 2 multiplied by
)
Can you now see that
and
...
So, in response to your original question:
means 7 multiplied by
...