SOLUTION: Please help with this problem. Z=sqrt((1000^2)+(1592^2)) It is my understanding that the square root of a "number" squared is the "number". If this is true I would solve this as

You can put this solution on YOUR website!
Start with the given equation.


Square 1000 to get 1,000,000. Square 1592 to get 2,534,464

Add


Take the square root of 3,534,464 to get approximately 1,880.02

You can put this solution on YOUR website!
Z=sqrt((1000^2)+(1592^2))
No, if there were a * (multiply) between them it would be 1000*1592
but if there's a plus or a minus you have to do the math inside the radical
then find the square root of that
:
You can prove this to yourself with a calc: Enter = 1880...

You can put this solution on YOUR website!
Evaluate:

While your statement - "...the square root of a 'number' squared is the 'number'." is true, your conclusion is faulty.
You can easily see this in the Pytagorean theorem:
Taking the square root of both sides we get...
and this is NOT the same as because the sum of the squares is not the same as the sum of the numbers, so...
Square the numbers under the radical sign.
Add the numbers under the radical sign.
Now extract the square root.
...and this is an irrational number (a non-repeating, non-terminating decimal).

You can put this solution on YOUR website!
Please help with this problem.
Z=sqrt((1000^2)+(1592^2))
It is my understanding that the square root of a "number" squared is the "number".
If this is true I would solve this as: Z=1000+1592 so Z=2592, but Im not sure this is correct

This is a very common error in mathematics. 

Notice that when there is only MULTIPLICATION under the radical,
what you did would have been correct: 

 is TRUE because




However, when there is ADDITION or SUBTRACTION 
under the radical, that does NOT WORK:  

 is FALSE because



            
So what you did won't work because of the PLUS SIGN 
under the radical.  If they had been MULTIPLIED under 
the radical, then you could have.

If the problem had been this   then the
answer would have been  and then 

However there was ADDITION under the radical, so you cannot
take individual square roots.  All you can do is do whatever 
you can under the radical FIRST.













That's the simplest radical form.

The approximate decimal value is



----------------------

Notice that 



Howver,



Math rules that work when things are MULTIPLIED or 
DIVIDED will NEVER work for things ADDED or 
SUBTRACTED.

and likewise:

Math rules that work for things ADDED or SUBTRACTED 
will NEVER work for things MULTIPLIED or DIVIDED.

Edwin