Cube Root

Cube root is a mathematical operation used to determine the number that, when multiplied by itself twice (cubed), results in a given value.

Table of contents:

Cube Root
Formula
Solved Examples
FAQs

Cube Root

Cube root is denoted by the symbol “∛”. For example, the cube root of 8 is 2, because 2 × 2 × 2 = 8.

Steps to Find the Cube Root

The formula for cube root is:

∛x = y

where x is the number whose cube root is to be found, and y is the cube root of x.

To find the cube root of a number, you can use the following steps:

Step 1: Start with the number whose cube root you want to find.

Step 2: Divide the number into groups of three digits starting from the rightmost digit. If there are any remaining digits that cannot form a group of three, add zeros to the left of the number to form a complete group of three.

Step 3: Find the cube root of the leftmost group of three digits. You can use a table of cube roots or a calculator to find this value.

Step 4: Write down the cube root of the leftmost group of three digits as the first digit of the cube root of the original number.

Step 5: Subtract the cube of the value found in Step 4 from the leftmost group of three digits.

Step 6: Bring down the next group of three digits to the right of the remainder obtained in Step 5. This forms a new number that is smaller than the original number.

Step 7: Repeat steps 3 to 6 until all the groups of three digits have been processed.

Step 8: The final answer is the cube root of the original number.

For example, to find the cube root of 474552, we can follow these steps:

Step 1: Start with the number 474552.

Step 2: Divide the number into groups of three digits: 474, 552.

Step 3 :- in place of ∛474 ≈ 8.04
∛474 ≈ 7.79

Step 5:- 474 – 7^3= 131.

Step 6:- in place of 86552. it should be 131552

Step 7 :- Now divide 1315 by product of 7 and 21. 1315/147= 8.9

Step 8:- The final answer is the cube root of the original number: ∛474552 ≈ 78.

Solved Examples

Example 1: Find the cube root of 27.

Solution:
We know that 3 × 3 × 3 = 27.
Therefore, the cube root of 27 is 3.
Answer: ∛27 = 3.

Example 2: Find the cube root of 125.

Solution:
We know that 5 × 5 × 5 = 125.
Therefore, the cube root of 125 is 5.
Answer: ∛125 = 5.

Example 3: Find the cube root of 1000.

Solution:
We can use the fact that 10 × 10 × 10 = 1000 to find the cube root of 1000.
Therefore, the cube root of 1000 is 10.
Answer: ∛1000 = 10.

Cube Root FAQS

Grade 8 Science Worksheets

• Earth & Space Science
• Physical Science
• Life Science
• Chemistry
• Structure of Atom (Basic)
• Fossils
• Bio Classification
• Sedimentary Rock
• Chemical Reaction
• Climate
• Compounds and Mixtures
• The Universe
• Dynamics of our solar system
• Organization of the universe, and its development
• Earth Systems
• Rocks and Fossils
• Sources of energy that power the subsystems and cycles of the dynamic earth: the geosphere, hydrosphere, atmosphere and biosphere
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• Structure and function of the cell.
• Chromosomes, genes, and the molecular basis of heredity
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• Understanding biological evolution
• How Living things are classified
• How Living Systems live
• Life Cycle of living things
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• States and properties of matter
• Changes in States Of Matter
• Chemical properties of Matter
• Structure of matter
• Conservation of matter
• Basics of chemical reactions
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