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# 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.

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## 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 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.

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## 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.

Example 2: Find the cube root of 125.

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

## Cube Root FAQS

##### What is the cube root of a negative number?

The cube root of a negative number is also a negative number. For example, the cube root of -8 is -2, because -2 × -2 × -2 = -8.

##### Can every number have a cube root?

Yes, every real number has a unique cube root. However, complex numbers may have multiple cube roots.

##### How can I calculate the cube root without a calculator?

You can calculate the cube root using long division method or by using an approximation method using a table of cube roots.

##### How can I simplify a cube root?

You can simplify a cube root by factoring the number inside the cube root into its prime factors and then taking out the factors that appear in groups of three. For example, ∛24 can be simplified as ∛8 × ∛3, which is equal to 2∛3.

##### What is the relationship between square roots and cube roots?

Square roots and cube roots are both types of roots, but square roots find the number that when multiplied by itself once gives the original number, while cube roots find the number that when multiplied by itself twice (cubed) gives the original number. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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