What is the perfect cube of 1331?

Find if the following number is a perfect cube?
1331

1331

∴ 1331 = 11 x 11 x 11 = (11)3
∴ 1331 is a perfect cube.

Concept: Concept of Cube Root

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Page 2

Find if the following number is a perfect cube?
24000

24000∵ 24000 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5

= (2)2 x (2)3 x (5)3 x 3

Concept: Concept of Cube Root

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Page 3

Find if the following number is a perfect cube?
1728

1728

∵ 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
= (2)3 x (2)3 x (3)3 
∵  1728 is a perfect cube.

Concept: Concept of Cube Root

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Page 4

Find if the following number is a perfect cube?
1938

1938

1938 = 2 x 3 x 17 x 19
1938 is not a perfect cube.

Concept: Concept of Cube Root

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 By grouping the digits, we get 1 and 331

We know that, since, the unit digit of cube is 1, the unit digit of cube root is 1.

∴ We get 1 as unit digit of the cube root of 1331.

The cube of 1 matches with the number of second group.

∴ The ten's digit of our cube root is taken as the unit place of smallest number.

We know that, the unit’s digit of the cube of a number having digit as unit’s place 1 is 1.

\therefore \sqrt[3]{1331}=11

 By grouping the digits, we get 4 and 913

We know that, since, the unit digit of cube is 3, the unit digit of cube root is 7.

∴ we get 7 as unit digit of the cube root of 4913.

We know 1^{3}=1 \text { and } 2^{3}=8 , 1 > 4 > 8.

Thus, 1 is taken as ten digit of cube root.

\therefore \sqrt[3]{4913}=17

 By grouping the digits, we get 12 and 167.

We know that, since, the unit digit of cube is 7, the unit digit of cube root is 3.

∴ 3 is the unit digit of the cube root of 12167

We know 2^{3}=8 \text { and } 3^{3}=27, 8 > 12 > 27.

Thus, 2 is taken as ten digit of cube root.

\therefore \sqrt[3]{12167}=23

 By grouping the digits, we get 32 and 768.

We know that, since, the unit digit of cube is 8, the unit digit of cube root is 2.

∴ 2 is the unit digit of the cube root of 32768.

We know 3^{3}=27 \text { and } 4^{3}=64, 27 > 32 > 64.

Thus, 3 is taken as ten digit of cube root.

\therefore \sqrt[3]{32768}=32

In math, the cube root of a number like 1331 is a number that, when multiplied by itself two times, is equal to 1331.

We would show this in mathematical form with the cube root symbol, which is similar to the radical symbol (√) used in a square root, but which also has the number 3 above the symbol (this number is called the index):

So, the √ is called the radical symbol, the little 3 above it is the index (which means multiply by itself two more times), and the number, 1331, is called the radicand.

To explain the cube root a little more, the cube root of the number 1331 is a number (which we call n) that when multiplied by itself twice is equal to 1331:

∛1331 is the same as 1331⅓ and so if you are solving a problem in a spreadsheet like Excel, Numbers, or Google Sheets, you can use =1331^(1/3) to calculate the cube root.

For the purposes of this article, we'll use a scientific calculator to work out the cubic root by typing the number 1331 and pressing the [∛x] button, to give the following answer:

Is 1331 a Perfect Cube?

When the cube root of a given number is a whole number, this is called a perfect cube. Perfect cubes are important for many mathematical functions and are used in everything from carpentry through to more advanced topics like physics and astronomy.

If we look at the number 1331, we know that the cube root is 11, and since this is a whole number, we also know that 1331 is a perfect cube.

If you want to learn more about perfect cube numbers we have a list of perfect cubes which covers the first 500 perfect cube numbers.

Is the Cube Root of 1331 a Rational or Irrational Number?

Another common question you might find when working with the roots of a number like 1331 is whether the given number is rational or irrational. Rational numbers can be written as a fraction and irrational numbers can't.

The quickest way to check if a number is rational or irrational is to determine if it is a perfect cube. If it is, then it's a rational number, but if it is not a perfect cube then it is an irrational number.

We already know that 1331 is a rational number then, because we know it is a perfect cube.

Rounding the Cube Root of 1331

Sometimes when you work with the cube root of 1331 you might need to round the answer down to a specific number of decimal places:

10th: ∛1331 = 11.0

100th: ∛1331 = 11.00

1000th: ∛1331 = 11.000

Simplifying the Cube Root of 1331

It is possible to simplify the cube root of 1331 if the radicand can be made smaller. When that is possible, it is called the cube root of 1331 in its simplest radical form.

In this example, the cube root of 1331 in its simplest form is:

Practice Cube Roots Using Examples

If you want to continue learning about cubic roots, take a look at the random calculations in the sidebar to the right of this blog post.

We have listed a selection of completely random numbers that you can click through and follow the information on calculating the cubic root of that number to help you understand number roots.

Calculate Cube Square Root Problem