Cube Root of 3

The cube root of a number is a value that, when multiplied by itself three times, results in the original number. For example, the cube root of 27 is 3 because 3 × 3 × 3=27. Cube roots are frequently used in mathematics, engineering, and physics to simplify equations and solve problems. This article will explore the cube root of 3 and its significance.

Introduction

The cube root of 3 is the number that, when multiplied by itself three times (cubed), equals 3. In other words, it is the value that, when raised to the power of 3, results in 3. Mathematically, the cube root of 3 is represented as x such that x3 = 3. To find the cube root of 3, we need to determine the value of x that satisfies this equation.

Defining the cube root of 3

The cube root of 3, denoted as cube root 3, is the real number that, when multiplied by itself three times, equals 3. This value satisfies the equation 33= 3. The cube root of 3 is not a whole number; it is approximately 1.442249.

Also Read: Factors of 81

Calculating Cube Root of 3

The cube root of 3 can be calculated using an approximation formula.

Approximation Formula: One common approximation formula for the cube root of 3 is 1 + (13) + (127) +.... where the series continues until the terms become negligible. This formula provides a close approximation of the cube root of 3.

Another approximation method is given below:

Let's now determine the value of 33 in a systematic, step-by-step method.

Assume that x is equivalent to the cube root of 3.

Then, x = 33

We already know that 13 = 1 and 23 = 8.

Consequently, x is between 1 and 8. However, if we look at a number line, it is closer to the number 1 than the number 8. As a result, we can assume a value, say 1.4, which is roughly the cube root of 3.

We must now divide 3 by an approximate number in order to find the value of 33.

3 divided by 1.4 comes in

31.4 = 2.1428

Once more, we must divide this number by 1.4.

Also Read: Factors of 96

When we divide, we receive,

2.14281.4 = 1.53

Obtaining the value of 33 requires calculating the average of 1.4, 1.4, and 1.53.

(1.4+1.4+1.53)3 = 1.44

The exact value of 33 is therefore 1.442219.

Consequently, 1.44 is almost equal to 1.442249.

Uses of Cube Root of 3

  • Geometry: Cube roots are often used in geometry, especially with 3-dimensional shapes. For instance, to find the volume of a cube, you multiply the length of one side by itself three times.
  • Engineering: In engineering, cube roots help solve problems related to forces and stresses in structures. For example, the stress in a cylinder under internal pressure involves the cube root of the radius.
  • Physics: Cube roots are utilized in physics, particularly in wave mechanics and acoustics. For example, the frequency of a standing wave in a closed pipe is proportional to the cube root of its length.

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Frequently Asked Questions on Cube Root of 3

Ans. The cube root of 3 is approximately 1.442.

Ans. The cube root formula for a number x is x3.

Ans. The cube of 3 is 33 = 27.