Grade 8 Radicals: Cube Roots

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A cube has a volume of 1728 cubic meters. How long is each edge (in meters)?

   1. A cube's volume is edge × edge × edge, so the edge is ∛1728: the number used 3 times as a factor to make 1728.
   2. 12 × 12 × 12 = 1728, so ∛1728 = 12.
   3. So each edge is 12 meters.

   Answer: 12

2. Example 2

   ∛433 is between two consecutive whole numbers. What is the smaller one?

   1. Find the perfect cubes on each side of 433: 7³ = 343 and 8³ = 512.
   2. 343 < 433 < 512, so 7 < ∛433 < 8.
   3. The smaller one is 7.

   Answer: 7

3. Example 3

   x³ = 1000. What is x?

   1. x³ = 1000 means x × x × x = 1000.
   2. 10 × 10 × 10 = 1000.
   3. So x = 10.

   Answer: 10