The cube root of 1000 is the number whose cube is 1000. Let x be the cube root of 1000, the ∛1000 = x and x3 = 1000. The sign “√” is called the radical sign, often used to represent the nth root of a number, and “∛” is used to represent the cube root of a number.
The cube root of 1000 in exponential form is written as (1000)1/3. Let us learn how to find the cube root of 1000.
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What Is the Cube Root of 1000?
The cube root of 1000 is the number whose cube is 1000. A perfect cube is a number which is the cube of an integer. Since the cube of 10 is 1000, 1000 is a perfect cube number. Learn the cube root of 1000, and also learn how to calculate the cube root of 1000.
Check out the cubes of numbers from 1 to 50.
How to Find the Cube Root of 1000?
Since 1000 is a perfect cube number, we can easily calculate the cube root of 1000 by the prime factorisation method.
Prime factorisation of 1000 = 2 × 2 × 2 × 5 × 5 × 5
To calculate the cube root, we have to make a group of three for each factor and take that factor one time.
Cube root of 1000 = ∛(2 × 2 × 2 × 5 × 5 × 5) = 2 × 5 = 10
Therefore, the cube root of 1000 is 10.
Video Lesson on Finding Cube Roots
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Solved Examples on Cube Root of 1000
Example 1:
Find a real root of the equation y3 – 1000 = 0.
Solution:
Given an equation, y3 – 1000 = 0
⇒ y3 = 1000
Taking cube roots on both sides, we get,
⇒ y = ∛1000
The cube root of 1000 is 10. A real cube root of the given equation is 10.
Example 2:
Find the length of the side of the cube whose volume is 1000 cm3.
Solution:
Let x be the side of the cube.
Volume of the cube = x3 = 1000 cm3
⇒ x = ∛1000 = 10 cm
Thus, the length of the sides of the given cube is 10 cm.
Example 3:
The volume of a cone is 1000𝜋 cm3. Find the base area of the cone whose height is three times its radius.
Solution:
Let r be the base radius of the cone.
The height of the cone = 3r
The volume of the = ⅓ 𝜋 r2 × 3r = 𝜋r3
⇒ 𝜋r3 = 1000𝜋
⇒ r3 = 1000 (taking cube roots on both sides)
⇒ r = ∛1000 = 10 cm
∴ base area of the cone = 𝜋r2 = 22/7× 102 = 220/7 cm2
Frequently Asked Questions on Cube Root of 1000
What is the cube root of 1000?
The cube root of 1000 is 10.
Is 1000 a perfect cube number?
Yes, 1000 is a perfect cube number. 103 = 1000.
Is the cube root of 1000 a whole number?
Yes, the cube root of 1000 is a whole number, and ∛1000 = 10.
Is the cube root of 1000 a rational number?
Yes, the cube root of 1000 is a rational number.
Can we find the cube root of 1000 by the prime factorisation method?
Yes, we can easily find the cube root of 1000 by the prime factorisation method.
How do you find the cube root of 1000?
The cube root of 1000 can be easily determined by prime factorising 1000.
What is the prime factorisation of 1000?
The prime factorisation of 1000 is 2 × 2 × 2 × 5 × 5 × 5.
