Question 150807
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
<pre><font size = 4 color = "indigo"><b>

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: 

{{{sqrt(3^2*4^2)=3*4}}} is TRUE because
{{{sqrt(9*16) = 12}}}
{{{sqrt(144) = 12}}}
{{{12=12}}}

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

{{{sqrt(3^2+4^2)=3+4}}} is FALSE because
{{{sqrt(9+16) = 7}}}
{{{sqrt(25) = 7}}}
{{{5=7}}}
            
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  {{{Z=sqrt((1000^2)(1592^2))}}} then the
answer would have been {{{Z=1000*1592}}} and then {{{Z=1592000}}}

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.

{{{Z=sqrt((1000^2)+(1592^2))}}}

{{{Z=sqrt(1000000+2534464)}}}

{{{Z=sqrt(3534464)}}}

{{{Z=sqrt(64*55226)}}}

{{{Z=sqrt(64)sqrt(55226)}}}

{{{Z=8sqrt(55226)}}}

That's the simplest radical form.

The approximate decimal value is

{{{Z=1880.017021}}}

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

Notice that 

{{{sqrt(A^2*B^2) = A*B}}}

Howver,

{{{sqrt(A^2 + B^2) <> A+B}}}

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</pre>