Cube Root 1 to 20

Cube Roots can be used for the many mathematical solving question. Some of the major application of the cube root has been observed in calculating the volume of geometrical shapes like cylinders, circles, cubes, etc.

Cube Root

It is a value when it is multiplied by itself three times; it gives the original value. For example, the cube root of 64 is expressed in the form of ∛64 Is 4. This is when four is

multiplied thrice by itself; it gives 64. Therefore, we can also conclude that the cube root produces the normally cubed value.

Symbol of Cube Root

The cube root symbol is expressed as ∛x.

Cube Root Formula

Assume that the cube root of "q" produces a value of "r" such that

∛q = r. The formula can only be validated when

q=r³

Cubes Value From 1 to 20

Methods to Find the Cube Root

One of the most preferred and easy methods is Prime factorization adopted to find the cube of the root of the given value. Let us understand with the example:

Number = 27

Prime factorisation of 27 = 3 x 3 x 3

Cube root will be = 3

Simplification of the Algebraic Cube Roots

The cubic radical should have the necessary conditions:

• It should not have a fractional number under the radical symbol
• Under the cube root symbol, it should not have a perfect power factor
• No exponent value should be greater than the index value in the cube root
• If the fraction comes into the radical, the fraction's denominator should not have any fraction.

Problems Based on the Cube Root

Question: Determine the Cube root of 64

Solution: Applying the prime factorization method, we can find the cube root of 64.

Prime factorisation of 64

64 = 2 x 2 x 2 x 2 x 2 x 2

64 = 2 x 2 = 4

Cube Root of 64 is 4

Question: Find out the cube root of 1331

Solution: Applying the prime factorization method:

1331 = 11 x 11 x 11

1331 = 11³

Cube Root of 1331 is 11

Question: What is the cube root of 216

Solution: Using the prime factorization method to get a suitable number of prime factors

216 = 2 x 2 x 2 x 3 x 3 x 3

216 = 2³ x 3³

216 = ( 2×3)³

216 = 6³

Cube Root of 216 is 6

Question: Find out the value of ∛1728

Solution: Applying the prime factorization method

1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

1728 = 2 x 2 x3

Value of ∛1728 is 12

Question: Determine the Cube of 3.5

Solution: 3. 5 x 3.5 x 3.5

= 42.875