When we refer to number less than one in this section, we mean in the range 0<n<1, not negative values.

Objective:

To find cubes and cube roots of numbers outside the normal range.

General:

• Finding cubes and cube roots of numbers less than 1 and greater than 1000 is done using the exact same process of the slide rule.  However, we will need to rewrite the number in an appropriate first.

Method for Cubes:

• Write the number in scientific notation.
• Determine the cube of the decimal part as normal.
• Multiply the exponent of the power of ten by three.
• Multiply the result from the rule by the new power of ten.

Method for Cube Roots:

• Write the number so that a power of ten divisible by 3 is the factored out without the decimal part not going less than 1.
• Determine the cube root as normal.
• Divide the index of the power of ten by three.
• Multiply the result from the rule by the new power of ten.

 

Example 1:  Find the value of 203³.

Write 203 in scientific notation giving 2.03 x 10².  Find the cube of 2.03 as normal.

• Move the cursor to D2.03
• Read the result K8.37 (first decade)
• Multiply the exponent by 3 giving 6.
• Multiply the result from the slide rule by 10⁶.
• Answer: 8.37 x 10⁶ = 8,370,000

 

Example 2:  Find the value of 0.00415³.

Write 0.00415 in scientific notation giving 4.15 x 10^-3.  Find the cube of 4.15 as normal.

• Move the cursor to D4.15
• Read the result K71.5 (second decade)
• Multiply the exponent by 3 giving -9.
• Multiply the result from the slide rule by 10^-9.
• Answer: 71.5 x 10^-9 = 0.0000000715

 

Example 3:  Find 3√84500.

The power of ten with exponent divisible by 3 that can be factored out is 10³, so we rewrite 84500 as 84.5 x 10³.

• Move the cursor to K84.5 (second decade)
• Read the result D4.39
• Divide the exponent by 3 giving 1.
• Multiply the result from the slide rule by 10¹.
• Answer: 4.39 x 10¹ = 43.9

 

Example 4:  Find 3√0.0000255.

The power of ten with exponent divisible by 3 that can be factored out is 10^-6, so we rewrite 0.0000255 as 25.5 x 10^-6.

• Move the cursor to K25.5 (second decade)
• Read the result D2.94
• Divide the exponent by 3 giving -2.
• Multiply the result from the slide rule by 10^-2.
• Answer: 2.94 x 10^-2 = 0.0294

 

Practice Questions:  Evaluate the following.

1. 56500³ (Ans: 181,000,000,000,000)
2. 0.00045³ (Ans: 0.000000000091)
3. ³√650000 (Ans: 86.6)
4. ³√0.0086 (Ans: 0.205)