Squares, Cubes and Their Roots

A small raised number is an exponent; it counts how many times the base is multiplied by itself.

• Squared: $8^2 = 8 \times 8 = 64$.
• Cubed: $4^3 = 4 \times 4 \times 4 = 64$.

Roots run the process backwards.

• The square root $\sqrt{121} = 11$, because $11^2 = 121$.
• The cube root $\sqrt[3]{27} = 3$, because $3^3 = 27$.

Numbers like $1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144$ are perfect squares; $1, 8, 27, 64, 125$ are perfect cubes.

Exam checkpoint

A square is a number multiplied by itself and a cube is a number multiplied by itself three times. Roots undo those operations. Build a small table of perfect squares ($1,4,9,16,25,36,49,64,81,100$) and useful cubes ($1,8,27,64,125$); this gives you fast assessment recall.

Short worked example. $\sqrt{81}=9$ because $9\times9=81$. Also $\sqrt[3]{64}=4$ because $4\times4\times4=64$.