Show that sqrt(27) + sqrt(192) = a*sqrt(b), where a and b are prime numbers to be determined

We want to get the the sqrt(27) and sqrt(192) so that they have the same number in the square so they can then be added together. We will look at the factorisation of 27, 192. We can see 27 is divisible by 3, 3x9, so we can say sqrt(27) = sqrt(3) * sqrt(9) as the sqrt(9) is 3, we can write sqrt(27) = 3* sqrt(3). Now we look at 192 and we want it to be in the form asqrt(3) so we look divide 192 by 3 to get 64. So we know sqrt(192) = sqrt(64)sqrt(3) as sqrt(64) = 8 we can write sqrt(64) as 8. Hence we have sqrt(192) = 8sqrt(3) so sqrt(192) + sqrt(27) = 8sqrt(3) + 3sqrt(3) = 11sqrt(3). Hence a,b equal 11,3 respectively and we can see that a,b are both prime.