[The_Reader_David]

Well then you didn’t multiply the numbers I gave you, only decimal approximations of them in your calculator.

Here we’ll do it the old school way, no decimal approximations, no calculators:

{[21/2 - sqrt(441/4 - 48)]/2}*{[21/2 + sqrt(441/4 - 48)]/2}

= [21/2 - sqrt(441/4 - 48)]*[21/2 + sqrt(441/4 - 48)]/4 (since ratios multiply by multiplying the numerators to give the new numerator, and the denominators to give the new denominator)

= [(21/2)^2 - (441/4 -48)]/4

(since as you should remember from HS algebra (a - b)*(a + b) = a^2 - b^2 and the square of a square root is whatever you took the square root of in the first place)

= (441/4 - 441/4 + 48)/4 (since squaring a ration squares the numerator and squares the denominator)

= 48/4 = 12.

[mmichaels1970]

I used a slide rule.