Cube Root of 4

The cube root of 4 is a value which on getting multiplied by itself, three times, results in the original number. It is expressed in the form of ‘3√4’. The meaning of cube root is basically the root of a number which is generated by taking the cube of another number. Hence, if the value of 3√4 = x, then x3 = 4 and we need to find here the value of x. Learn how to find cube root using the prime factorisation and estimation method.

Cube root of 4, 3√4 = 1.5874

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Calculation of Cube Root of 4

Since 4 is not a perfect cube, hence we cannot use here prime factorisation method or estimation method to find the cubic root of 4. Therefore, we are going to use another method here which is called the Newton Raphson method. Here are the following steps for the same.

  • As per this method, we will assume a number, say n, which is equal to the cube root of 4.
  • Now, divide 4 by n and then divide its quotient again by n.
  • Take the average of n and the two quotients obtained by division method. This value will be almost nearer to the value of 3√4.
  • For more accurate value, we will repeat the method.

Now let us move ahead to find the value of 3√4.

Let us assume here n=2 equal to the cube root of 4.

So,

4/2 = 2

& 2/2 = 1

Hence, we get here three numbers to generate the average.

Take the average of 2 (assumed number), 2 (first quotient) and 1 (second quotient).

(2+2+1)/3 = 5/3 = 1.67

This value is almost near to the actual value of 3√4, i.e. (1.5874)

Hence, we will repeat the method here by assuming n=1.6.

Thus,

4/1.6 = 2.5

& 2.5/1.6 = 1.5625

Hence, by taking the average of 1.6, 1.6 and 1.5625, we get;

(1.6+1.6+1.5625)/3 = 4.7625/3 = 1.5875.

Therefore, we get the value of the cube root of 4 equal to 1.5875, which is an almost accurate number.

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