Trick to Find Cube Root of 4 Digit Number

A cube root is related to a number that can be obtained by multiplying this root with itself three times to yield the specified value. The cube root of a number is written as where x is the given number.

The formula for cube root is simple but important in higher-level mathematics:

such that m³ = x

For example, the cube root of 8 is 2 because 2³=8.

Unit Digit Table for Cube Roots

The following table represents the unit digit of the cube root based on the unit digit of the given 4- digit number:

All perfect cube 4 digit numbers are:

How to Find Cube Root of a 4-Digit Number using Trick

This method works best for perfect cubes. Here's how to quickly find the cube root of any 4-digit number using an example:

Step 1: Identify the Unit Digit

Example: Find the cube root of 4096. The unit digit is 6. From the cubes of numbers 1 to 10, we know that a cube with the unit digit 6 has a cube root ending in 6.

Step 2: Ignore the Last Three Digits

Remove the last three digits of the number. For 4096, you are left with 4.

Now, find two perfect cubes between which this number lies and choose the smaller number. In this case, 1³=1 and 2³=8. Since 4 lies between 1 and 8 so the tens digit of the cube root will be 1.

Step 3: Combine the Digits

Now that you have both the unit digit (6) and the tens digit (1), the cube root of 4096 is 16.

Trick for Non-Perfect Cubes

The tricks discussed above apply mainly to perfect cubes. However, for numbers that are not perfect cubes, an estimation method can be used:

Find the nearest perfect cubes: Identify two perfect cubes between which the given number lies. For example, if you're asked to find the cube root of 70,000, note that:

• 41³=68,921
• 42³=74,088

Therefore, the cube root of 70,000 lies between 41 and 42.

Estimate the Cube Root:

• Since 70,000 is closer to 68,921, the cube root would be slightly greater than 41.
• Use interpolation or estimation to refine the cube root further if needed.

This approach helps to estimate cube roots of non-perfect cubes quickly, especially when an exact value isn't necessary.

Solved Examples on Cube Root of 4 Digit Number

Example 1: Find the cube root of 3375.

Solution:

Unit Digit: The unit digit of 3375 is 5. The cube root of a number ending in 5 will also end in 5.

Remaining Number: Remove the last three digits, leaving 3.

Compare: 1³=1 and 2³=8, and since 3 lies between 1 and 8, the tens digit of the cube root is 1.

Answer: Cube root of 3375 is 15.

Example 2: Find the cube root of 5832.

Solution:

Unit Digit: The unit digit of 5832 is 2, so the cube root ends in 8.

Remaining Number: Remove the last three digits, leaving 5.

Compare: 1³=1 and 2³=8, and since 5 lies between 1 and 8, the tens digit is 1.

Answer: Cube root of 5832 is 18.

Example 3: Find the cube root of 2197.

Solution:

Unit Digit: The unit digit of 2197 is 7, so the cube root ends in 3.

Remaining Number: Remove the last three digits, leaving 2.

Compare: 1³=1 and 2³=8, and since 2 lies between 1 and 8, the tens digit is 1.

Answer: Cube root of 2197 is 13.

Worksheet on Cube Root of 4 Digit Number

You can download free worksheet on cube root of 4 digit number from below:

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