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Last updated on November 30th, 2024

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Cube Root of 1331

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Foundation
Intermediate
Advance Topics

The cube root of 1331 is the value which, when multiplied by itself three times (cubed), gives the original number 1331. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, designing structures, density and mass, used in day-to-day mathematics like exponents, etc.

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What Is the Cube Root of 1331?

The cube root of 1331 is 11. The cube root of 1331 is expressed as βˆ›1331 in radical form, where the β€œ βˆ› β€œ  sign" is called the β€œradical” sign. In exponential form, it is written as (1331)1/3. If β€œm” is the cube root of 1331, then, m3=1331. Let us find the value of β€œm”.
 

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Finding the Cube Root of 1331

The cube root of 1331 can be found through various methods like:

 

  • Prime Factorization method

 

  • Subtraction method
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Cube Root of 1331 by Prime Factorization method

The steps involved to find βˆ›1331 are

 

  • Find the prime factors of 1331

 

  • After factoring 1331, make groups of three same factors out of the prime factors to get the cube root.


1331 = 11Γ—11Γ—11


βˆ›1331 = βˆ›(11Γ—11Γ—11)

 

  • After grouping together three same factors at a time, put the remaining factor under βˆ›.


Here, for 1331, no remaining factors are there. We get one group of prime factor 11, i.e., (11Γ—11Γ—11).


So, 1331 is a Perfect cube. βˆ›1331=11.
 

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Cube Root of 1331 By Subtraction Method

The subtraction method involves subtracting successive odd numbers repeatedly. 


Subtract the list of odd numbers β†’ 1,7,19,37,61,91,127,169,217,271,331,397……..successively till we get a zero.


Step 1 β€” Subtract the 1st odd number : 1331–1 = 1330 


Step 2 β€” Subtract the next odd number: 1330–7 = 1323


Step 3 β€” Subtract the next odd number: 1323–19 = 1304


Step 4 β€” Subtract the next odd number: 1304–37 = 1267


Step 5 β€” Subtract the next odd number: 1267-61 = 1206


Step 6 β€” Subtract the next odd number: 1206-91 = 1115


Step 7 β€” Subtract the next odd number: 1115-127 = 988


Step 8 β€” Subtract the next odd number: 988-169 = 819


Step 9 β€” Subtract the next odd number: 819-217 = 602


Step 10 β€” Subtract the next odd number: 602-271=331


Step 11 β€” Subtract the next odd number: 331-331=0

 

Here, the subtraction took place 11 times to reach zero.


Hence, the cube root of 1331 is 11. 
 

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Common Mistakes and How to Avoid Them in the Cube Root of 1331

Misconceptions or mistakes are common, so let us see how we can avoid those from happening. Here are some misconceptions listed below with their respective solutions.

Mistake 1

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When doing successive subtraction method for finding the cube root, students might have a doubt of why the list of odd numbers not in simple order as that of a general odd number list.

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The list of odd numbers that we have to subtract successively is a well researched list, for the sake of finding cube roots. Hence, students should follow that list.
 

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Cube Root of 1331 Examples

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Problem 1

Find ((βˆ›343/ βˆ›1331) Γ— (βˆ›512/ βˆ›1331))

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((βˆ›343/ βˆ›1331) Γ— (βˆ›512/ βˆ›1331)) 

 

=(7/ 11)Γ— (8/ 11)


=56/121

 

Answer: 56/121
 

Explanation

Simplified the expression and found the answer.
 

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Problem 2

The length, breadth, and height of a cuboid is 9 units, 4 units, and 5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 1331 cubic units.

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Volume of a cuboid = length Γ— breadth Γ— height = 9 Γ— 4 Γ— 5 cubic units = 180 cubic units.


Given, Volume of a cube = 1331 cubic units


β‡’ side Γ— side Γ— side = 1331 cubic units


β‡’ side =  βˆ›1331


β‡’ side = 11 units


Answer: Volume of the cuboid = 180 cubic units

 

Side length of the cube = 11 units

Explanation

Applied the formula and concept of the volume of a cuboid and cube and solved.
 

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Problem 3

Multiply βˆ›1331 / βˆ›216

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βˆ›1331/βˆ›216

 

= 11/6


Answer: 11/6
 

Explanation

We know that the cubic root of 216 is 6, hence dividing βˆ›1331 by  βˆ›216.
 

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Problem 4

What is βˆ›(1331)⁢* 1/6 ?

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 βˆ›(13316Γ—1/6)

 

= (1331)1/3

 

= 11


Answer: 11 
 

Explanation

We solved and simplified the exponent part first using the fact that, (13316Γ—1/6)=1331, then solved.
 

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Problem 5

Find βˆ›(1000-(-331)).

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 βˆ›(1000-(-331))

 

= βˆ›(1000+331)

 

=βˆ›1331

 

=11


Answer: 11
 

Explanation

Simplified the expression, and found out the cubic root of the result. 

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FAQs on 1331 Cube Root

1.What is the factorization of 1331?

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2.How to find the cube root of 1331 without factorization?

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3.What is the square root of 1331 by factorization method?

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4.Is 1331 a perfect cube by applying Prime Factorization method?

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5.How to find cube roots?

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Important Glossaries for Cubic Root of 1331

  • Prime Factorization - Expressing the given expression as a product of its factors, precisely its prime factors. Ex: 48=2  Γ— 2  Γ— 2  Γ— 2  Γ— 3

 

  • Perfect and non-perfect cube numbers - Perfect cube numbers are those numbers whose cube roots do not include decimal places. Ex: 8,343,512.

 

  •  Non-perfect cube numbers are those numbers whose cube roots comprise decimal places. Ex :7, 340, 500

 

  • Square root -The square root of a number is a value β€œy” such that when β€œy” is multiplied by itself β†’ y Γ— y, the result is the original number.

 

  • Rational numbers and Irrational numbers - The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.

 

  • Approximation - Finding out a value which is nearly correct, but not perfectly correct.

 

  • Iterative method - This method is a mathematical process which uses an initial value to generate further and step-by-step sequence of solutions for a problem. Here, Subtraction method is an example of iterative method.
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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