Powers and roots · Grade 7

In Grade 7 you learn: powers and index notation; square roots and cube roots.

A power tells you how many times to multiply a number by itself: 5^2 = 5 × 5 and 2^3 = 2 × 2 × 2. Square roots and cube roots undo squaring and cubing. Squares and cubes appear whenever we work with area and volume.

Key facts

• a^2 means a × a (a squared); a^3 means a × a × a (a cubed). Not a × 2!
• Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 …
• Cube numbers: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000 …
• √49 = 7 because 7^2 = 49; ∛64 = 4 because 4^3 = 64.
• A negative number squared is positive: (−4)^2 = 16, but −4^2 = −16.
• Estimate a root from the squares either side: √50 is just over 7.

Worked examples

Other years

• Powers and roots · Grade 6
• Powers and roots · Grade 8
• Powers and roots · Grade 9