Surds and Indices

Surds and Indices

Indices:

a^m * a^n = a^(m+n)
a^m / a^n = a^(m-n)
(a^m)^n = a^(mn)
(ab)^n = a^n b^n
a^0 = 1
a^-n = 1/a^n

Surds:

sqrt(ab) = sqrt(a)*sqrt(b)
sqrt(a/b) = sqrt(a)/sqrt(b)

Rationalization:

1/(a + sqrt(b)) = (a - sqrt(b))/(a^2 - b)

Useful squares:

n	n^2	n	n^2
11	121	21	441
12	144	22	484
13	169	23	529
14	196	24	576
15	225	25	625
16	256	26	676
17	289	27	729
18	324	28	784
19	361	29	841
20	400	30	900