Cube Root of 1000

Cube Root of 1000 is 10. Cube Root can be defined as the number that is multiplied twice to get the result. This means 10 when multiplied with itself twice it gives the product 1000. Cube root is represented by the symbol ∛. Learn how to find the cube root of 1000 in this article.

What is Cube Root of 1000?

Cube Root of 1000 is the number which when twice multiplied with itself results give the product 1000. If we start checking from 1, we find that 10 is the number which when multiplied twice with itself gives the product 1000. Hence, 10 is the cube root of 1000. We can represent cube root of 1000 as follows:

• Radical Form: ∛1000 = 10
• Fractional Exponential Form: (1000)^1/3 = 10

Cube Root of 1000 Calculator

Try out the following calculator to calculate the cube root of 1000:

How to Find Cube Root of 1000

Cube Root of 1000 can be found by following two methods

• Cube Root of 1000 by Prime Factorization Method
• Cube Root of 1000 by Repeated Subtraction Method

Cube Root of 1000 by Prime Factorization

Follow the following steps to find the cube root of 100 by Prime Factorization method

Step 1: Write the number in terms of prime factors i.e. 1000= 2 × 2 × 2 × 5 × 5 × 5

Step 2: Group the numbers in set of three. Hence, ∛1000 = ∛{(2 × 2 × 2) × (5 × 5 × 5)}

Step 3: Using Rules of Exponent, ∛1000 = ∛{(2)³ × (5)³} = {(2³)^1/3} × {(5³)^1/3} = 2 × 5 = 10

Hence, cube root of 1000 is 10.

Cube Root of 1000 by Repeated Subtraction Method

To find the cube root of 1000 we need to successively subtract 1000 by the numbers such as 1, 7, 19, 37, 61, 91, 127 and so on. The number of steps in which difference becomes zero is the cube root. Let’s see how it proceeds

• 1000 – 1 = 999
• 999 – 7 = 992
• 992 – 19 = 973
• 973 – 37 = 936
• 936 – 61 = 875
• 875 – 91 = 784
• 784 – 127 = 657
• 657 – 169 = 488
• 488 – 217 = 271
• 271 – 271 = 0

Here, we see that the we started subtracting from 1000 and the difference becomes zero in the tenth step. Hence, the cube root of 1000 is 10.

Is Cube Root of 1000 Irrational?

No, the cube root of 1000 is not an irrational number. The cube root of 1000 is 10 which is an inetger and 10 can be written as a fraction (10/1) as the numberator and denominator. Hence, cube root of 1000 is not irrational but rational.

Learn More,

• Cube and Cube Roots
• Perfect Cube
• Cube Roots from 1 to 30

Cube Root of 1000 Frequently Asked Questions

What is the Value of Cube Root of 1000?

The cube root of 1000 is 10.

Is Cube Root of 1000 Rational or Irrational?

The cube root of 1000 is 10 which is a rational number. Hence, the cube root of 100 is Rational

How to Calculate Cube Root of 1000?

Cube root of 1000 can be calculated by Prime Factorization and repeated subtraction method

Is 1000 a Perfect Cube?

The cube root of 1000 is 10 which is a perfect integer value hence 1000 is a perfect cube.

Is -10 the Cube Root of 1000?

No the cube root of 1000 is 10 not -10 as -10 × -10 × -10 = -1000

Whats the Cube Root of -1000?

The cube root of -1000 is -10.