A cube root of a number is a value that, when multiplied by itself three times, produces that number. For example, the cube root of 64 is 4, because 4 x 4 x 4 = 64.

Some examples of cube roots:

1. The cube root of 8 is 2 because 2 x 2 x 2 = 8. 2. The cube root of 27 is 3 because 3 x 3 x 3 = 27. 3. The cube root of 64 is 4 because 4 x 4 x 4 = 64. 4. The cube root of 125 is 5 because 5 x 5 x 5 = 125. 5. The cube root of 343 is 7 because 7 x 7 x 7 = 343. 6. The cube root of 1000 is 10 because 10 x 10 x 10 = 1000. 7. The cube root of 1728 is 12 because 12 x 12 x 12 = 1728. 8. The cube root of 2197 is 13 because 13 x 13 x 13 = 2197. 9. The cube root of 2744 is 14 because 14 x 14 x 14 = 2744. 10. The cube root of 4913 is 17 because 17 x 17 x 17 = 4913.

Symbol of Cube Root

The cube root symbol is represented by the radical symbol (√) with a small 3 written above it. i.e., ?.

Example: To find the cube root of a number, we simply write the number under the radical symbol and the 3 to the right.

For example, to find the cube root of 27, we write: ?27 = 3

This means that 3 is the cube root of 27.

In other words, 3 x 3 x 3 = 27.

Formula for Cube Root

The formula for the cube root of a number x is given as:

?x = y, where y is the cube root of x. y^{3} = x

Cube Roots from 1 to 30

The below charts show the cube root values for numbers 1 to 30. Students must learn the cube root values for 1 to 30 from charts to improve computation accuracy and speed. Mastering the concept behind cube roots is important for reducing errors in complex calculations.

Table of Cube Roots Values from 1 to 30

The table for cube root values for numbers 1 to 30 which are given below.

How to find the Cube Root for Numbers 1 to 30?

Students can find the cube root for numbers 1 to 30 using different methods such as:

Estimation method

Prime Factorization method

Long Division method

Cube Root by Prime Factorization Method

To find the cube root of a number using prime factorization method, follow these steps:

1. Write the given number in prime factorization form.

2. Group the factors in threes, starting from the right-most digit.

3. The cube root of the number is the product of the cube roots of the groups of factors.

For example, let's find the cube root of 27000 using prime factorization method:

1. Prime factorization of 27000: 27000= 2³ x 3³ x 5³

2. Group the factors in threes: 2³ x (3 x 3 x 3) x (5 x 5 x 5) = 2³ x 3³ x 5³

3. The cube root of the number is the product of the cube roots of the groups of factors: ?2³ x ?3³ x ?5³ = 2 x 3 x 5 = 30

Therefore, the cube root of 27000 is 30.

Cube Root by Long Division Method

To find the cube root of a number using the long division method, follow these steps:

1. Divide the given number into groups of three digits starting from the right-most digit. If there are any leftover digits at the beginning, add zeros to the left to form complete groups of three digits.

2. Find the largest cube that is less than or equal to the left-most group of three digits and write down the cube root of that number as the first digit of the cube root of the original number.

3. Subtract the cube of the digit found in step 2 from the left-most group of three digits and bring down the next group of three digits to the right of the remainder.

4. Double the digit found in step 2 and write it down as a temporary divisor under the remainder from step 3.

5. Divide the divisor into the first two digits of the remainder and write the result as the next digit of the cube root. This will be a single digit.

6. Multiply the last digit of the current partial cube root by the divisor and subtract the product from the dividend.

7. Bring down the next group of three digits from the original number to the right of the remainder.

8. Repeat steps 4-7 until all groups of three digits have been used.

Example: Let’s find the cube root of 91125 using the long division method:

Cube root of 91125 = 45.

Cube Root by Estimation Method

The estimation method for finding the cube root of a number involves making an educated guess and then refining that guess until it is as close as possible to the actual cube root.

Here are the steps for finding the cube root of a number using the estimation method:

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

Step 2: Start with an estimate for the cube root. This estimate should be a number that is close to the actual cube root. For example, if you want to find the cube root of 27, you could start with an estimate of 3, since 3^{3} = 27.

Step 3: Cube the estimate to see if it is close to the original number. In the example above, 3^{3} = 27, so the estimate is correct.

Step 4: If the estimate is not correct, adjust it based on how far off it was. For example, if you were trying to find the cube root of 1000 and your estimate was 10, you would see that 10^{3} = 1000, so your estimate is correct. However, if your estimate was 9, you would see that 9^{3} = 729, which is too low. To adjust your estimate, you would try a larger number, such as 11, since 11^{3} = 1331, which is too high. Based on these results, you could refine your estimate to be between 10 and 11.

Step 5: Repeat steps 3 and 4 until you get an estimate that is as close as possible to the actual cube root.

Using this method, you can estimate the cube root of any number. Keep in mind that the closer your initial estimate is to the actual cube root, the fewer iterations you will need to get an accurate estimate.

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