Question 150807
Evaluate:
{{{Z = sqrt((1000^2)+(1592^2))}}}
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:
{{{c^2 = a^2+b^2}}} Taking the square root of both sides we get...
{{{c = sqrt(a^2+b^2)}}} and this is NOT the same as {{{c = a+b}}} because the sum of the squares is not the same as the sum of the numbers, so...
{{{Z = sqrt((1000^2)+(1592^2))}}} Square the numbers under the radical sign.
{{{Z = sqrt(1000000+2534464)}}} Add the numbers under the radical sign.
{{{Z = sqrt(3534464)}}} Now extract the square root.
{{{Z = 1880.017}}}...and this is an irrational number (a non-repeating, non-terminating decimal).