Cube root of 729

The cube root of 729 is 9. The cube root of 729 is expressed as ∛729 in radical form, where the “∛"  sign is called the “radical” sign. In exponential form, it is written as (729)^⅓
 

We can find the cube root of 729, mainly through two methods: 

• Prime Factorization method.

• Subtraction method.

Finding a cube root of 729 through the Prime Factorization method involves determining the factor of 729.

Step 1 — Find the prime factors of 729. 

So 729 = 3×3×3×3×3×3

Step 2 — Group the factors of 729 in a group of 3.

Step 3 — Since 729 is a perfect cube, we have two pairs of 3 digits.

The cube root of 729 can be written as ∛729 = ∛(3×3×3)×(3×3×3) = 3×3 = 9 

Therefore, the cube root of 729 is 9.

The subtraction method involves subtracting successive odd numbers repeatedly. 

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

Step 1 — Subtract the 1st odd number : 729–1 = 728 

Step 2 — Subtract the next odd number: 728–7 = 721

Step 3 — Subtract the next odd number: 721–19 = 702

Step 4 — Subtract the next odd number: 702–37 = 665

Step 5 — Subtract the next odd number: 665-61 = 604

Step 6 — Subtract the next odd number: 604-91 = 513

Step 7 — Subtract the next odd number: 513-127 = 386

Step 8 — Subtract the next odd number: 386-169 = 217

Step 9 — Subtract the next odd number: 217-217 = 00

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

Hence, the cube root of 729 is 9. 

729-1 = 728

728-7 = 721

721-19 = 702

702-37 = 665

665-61 = 604

604-91 = 513

513-127 = 386

386-169 = 217

217-217 = 00 
 

• Exponent :The power to which the number is raised. In (729)^⅓, 1/3 is the exponent. 

• Irrational number:A number that cannot be expressed as a simple fraction.

• Rational number: A number that can be expressed as the quotient of two integers. 

• Inverse operations:An operation that reverses the effect of another operation.