Chat with our AI personalities
If there is only the radical, sqrt(b), in the denominator, the form of the fraction is sqrt(b)/sqrt(b).If the denominator is of the form a + sqrt(b) then the form of the fraction is [a - sqrt(b)]/[a - sqrt(b)].It is also possible to use [-a + sqrt(b)]/[-a + sqrt(b)], and this form may be preferred is a^2 < b.
sqrt(145) = sqrt(5)*sqrt(29), which is not a particularly simpler form!
sqrt(72) = sqrt(36*2) = sqrt(36)*sqrt(2) = 6*sqrt(2).
sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)
sqrt(52) = sqrt(4*13) = sqrt(4)*sqrt(13) = 2*sqrt(13).