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Last updated on November 30th, 2024

Cube Root of 1331

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.

What Is the Cube Root of 1331?

The cube root of 1331 is 11. The cube root of 1331 is expressed as ∛1331 in radical form, where the “ ∛ “ sign" is called the “radical” sign. In exponential form, it is written as (1331)^1/3. If “m” is the cube root of 1331, then, m³=1331. Let us find the value of “m”.

Finding the Cube Root of 1331

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

Prime Factorization method

Subtraction method

Cube Root of 1331 by Prime Factorization method

The steps involved to find ∛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 = 11×11×11

∛1331 = ∛(11×11×11)

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

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

So, 1331 is a Perfect cube. ∛1331=11.

Cube Root of 1331 By Subtraction Method

The subtraction method involves subtracting successive odd numbers repeatedly.

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

Step 1 — Subtract the 1st odd number : 1331–1 = 1330

Step 2 — Subtract the next odd number: 1330–7 = 1323

Step 3 — Subtract the next odd number: 1323–19 = 1304

Step 4 — Subtract the next odd number: 1304–37 = 1267

Step 5 — Subtract the next odd number: 1267-61 = 1206

Step 6 — Subtract the next odd number: 1206-91 = 1115

Step 7 — Subtract the next odd number: 1115-127 = 988

Step 8 — Subtract the next odd number: 988-169 = 819

Step 9 — Subtract the next odd number: 819-217 = 602

Step 10 — Subtract the next odd number: 602-271=331

Step 11 — 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.

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 × 2 × 2 × 2 × 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 “y” such that when “y” is multiplied by itself → y × 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.