Powers, Roots and Standard Form

Number

Recognising them

Multiplying any integer by itself produces a square number
Recognising them on sight is what makes surds, factorising and Pythagoras quick, so the first fifteen are worth committing to memory

n	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
n²	1	4	9	16	25	36	49	64	81	100	121	144	169	196	225

Multiplying an integer by itself twice over produces a cube number

n	1	2	3	4	5	10
n³	1	8	27	64	125	1000

The square root of an integer that is not a square number is irrational, and is called a surd
- √11 is a surd, whereas √121 is simply 11

Exam tip

The syllabus asks for recall, and it says which: squares and their roots from 1 to 15, and cubes and their roots of 1, 2, 3, 4, 5 and 10. On the non-calculator papers those are expected to be known rather than worked out.