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).
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.
Expressed as a surd in its simplest form, sqrt(234) = 3 sqrt(26).
sqrt(145) = sqrt(5)*sqrt(29), which is not a particularly simpler form!
sqrt(300n11) = sqrt(100n10*3n) = sqrt(100n10)*Sqrt(3n) = 10n5*sqrt(3n)
174 is an integer and not a fraction. However, it can be expressed in rational form as 174/1.
The SQRT(18) in radical form is 3*SQRT(2), where SQRT represents the radical symbol.
sqrt(72) = sqrt(36*2) = sqrt(36)*sqrt(2) = 6*sqrt(2).
sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)
It is: 87/174 = 1/2
sqrt(162) = sqrt(81*2) = sqrt(81)*sqrt(2) = 9*sqrt(2)
sqrt(52) = sqrt(4*13) = sqrt(4)*sqrt(13) = 2*sqrt(13).
sqrt(338) = sqrt(2*169) = sqrt(2)*sqrt(169) = 13*sqrt(2)