The cube root of 1331 is the number that is when multiplied three times to itself gives the result 1331. Let x be the cube root of 1331, the ∛1331 = x and x3 = 1331. The sign “√” is called the radical often used to represent the square root of a number and “∛” is used to represent the cube root of a number.
The cube root of 1331 in exponential form is written as 13311/3. Let us learn how to find the cube root of 1331.
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Cube Root of 1331 |
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Cube of 1331 |
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What is the Cube Root of 1331?
The cube root of 1331 is the number whose cube is 1331. A perfect cube is a number which is the cube of an integer. Since the cube of 11 is 1331, therefore 1331 is a perfect cube number. Learn the cube root of 1331 and also learn how to calculate the cube root of 1331.
Check the cubes of numbers from 1 to 50.
How to Find the Cube Root of 1331?
Since 1331 is a perfect cube number, we can easily calculate the cube root of 1331 by the prime factorisation method.
Prime factorisation of 1331 = 11 × 11 × 11
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 1331 = ∛(11 × 11 × 11) = 11
Therefore, the cube root of 1331 is 11.
Video Lesson on Finding Cube Roots
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Solved Examples on Cube Root of 1331
Example 1:
Find a real root of the equation y3 – 1331 = 0.
Solution:
Given an equation, y3 – 1331 = 0
⇒ y3 = 1331
Taking cube roots on both sides, we get,
⇒ y = ∛1331
The cube root of 1331 is 11. A real cube root of the given equation is 11.
Example 2:
Find the length of the side of the cube whose volume is 1331 cm3.
Solution:
Let x be the side of the cube.
Volume of the cube = x3 = 1331 cm3
⇒ x = ∛1331 = 11 cm
Thus, the length of the sides of the given cube is 11 cm.
Example 3:
The volume of a cone is 1331𝜋 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 cone = ⅓ 𝜋 r2 × 3r = 𝜋r3
⇒ 𝜋r3 = 1331𝜋
⇒ r3 = 1331 (taking cube roots on both the sides)
⇒ r = ∛1331 = 11cm
∴ base area of the cone = 𝜋r2 = 22/7× 112 = 2662/7 cm2.
Frequently Asked Questions on Cube Root of 1331
What is the cube root of 1331?
The cube root of 1331 is 11.
Is 1331 a perfect cube number?
Yes, 1331 is a perfect cube number, 113 = 1331.
Is the cube root of 1331 a whole number?
Yes, the cube root of 1331 is a whole number ∛1331 = 11.
Is the cube root of 1331 a rational number?
Yes, the cube root of 1331 is a rational number.
How do you find the cube root of 1331?
The cube root of 1331 can be easily determined by prime factorising 1331.
What is the prime factorisation of 1331?
The prime factorisation of 1331 is 11 × 11 × 11.
