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”.
 

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

 

• Prime Factorization method

 

• Subtraction 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.
 

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. 
 

• 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.