Cube root of 64

The cube root of 64 is 4. The cube root of 64 is expressed as ∛64 in radical form, where the “∛"  sign is called the “radical” sign. In exponential form, it is written as (64)^⅓
 

We can find the cube root of 64, mainly through two methods: 

i) Prime Factorization method.

ii) Subtraction method.
 

Finding a cube root of 64 through the Prime Factorization method involves determining the factor of 64.

Step 1 — Find the prime factors of 64. 

So, 64 = 2×2×2×2×2×2

Step 2 — Group the factors of 64 together in a group of 3(i.e., power of 3).

Step 3 — Here, we get two triplet groups of factor 2 in the power of 3, i.e., 2³ or 2×2×2 

The cube root of 64 can be written as ∛64 = ∛(2×2×2)×(2×2×2) = 2×2 = 4 

Therefore, the cube root of 64 is 4.

This method involves subtracting successive odd numbers repeatedly. The list of odd numbers that should be subtracted successively are →

1,7,19,37,61,91,127,169,217,331,397 … This iteration will continue till we get a zero. 

Step 1 — Subtract the 1st odd number : 64–1 = 63 

Step 2 — Subtract the next odd number: 63–7 = 56

Step 3 — Subtract the next odd number: 56–19 = 37

Step 4 — Subtract the next odd number: 37–37 = 00

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

Hence, the cube root of 64 is 4. 
 

• Cubic root —  The number when multiplied with itself 3 times gives the original number is called as Cubic root.

• Prime Factorization — Find out prime factors for given number.

• Exponent — The number to which the power is raised. In (64)^⅓, ⅓ is the exponent.

• Irrational number – A number that does not follow the definition of rational.