Numbers – Square, Cube Numbers and their Roots

Square numbers – the result of multiplying an integer (whole number) by itself

. e.g 25 is a square number because it’s the result of 5 x 5

. This is written as 52 → five squared or five to the power of two (5²)

. Negative numbers can also be squared because when multiplying two negative numbers the result is positive 

. The answer of a negative number squared is the same as if it was positive e.g (-4)² is the same as 4² as they both equal 16

. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 → first 12 square numbers

Square root – the square root of a number is a value, when multiplied by itself, gives the original number

. e.g the square root of 49 is ±7 because 7² = 49 and -7² = 49

. Square root symbol is √

Cube number – the result of multiplying an integer (whole number) by itself 3 times

. e.g 64 is a cube number because it’s a result of 4 x 4 x 4

. This is written as 43– four cubed or four to the power of three

. Negative numbers cannot be cubed because odd x odd x odd results in a odd number (-4)3 64

. 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 > first 12 cube numbers

Cube root – cube root of a number is a value, when cubed, gives the original number

. e.g the cube root of 125 is 5 because 5 x 5 x 5 = 125

. Cube root symbol is ³√

Example:

Q) Workout the value of (2³ × 6) ÷ ³√64

1.  Using BIDMAS, deal with the indices first 2³ = 8 and ³√64 = 4
2. Workout the numerator 48 and divide by 4 (denominator) 

A) 12

Tips:

. Another way of writing cube root or square root is to put the number to the power of (1/3) or ½ 

. e.g. ³√64 can be written as 64¹/³ and √16 can be written as 16¹/²