Cube Root of 47

Cube Root of 47 is approximately 3.6088. This means that the number which, when cubed (raised to the power of three), equals 47 is approximately 3.61. In this article, we will discuss all the things related cube root of 47.

👁 Cube-Root-of-47

Cube Root Definition

Cube root is a mathematical operation signified by the symbol ∛, employed for finding a number as a result of whose multiplication by itself three times (or cube) gives a given number.

In another way, y = ∛x ,then y × y × y = x the cube root is the reciprocal of cubing.

What is Cube Root of 47?

Cube root of 47 rounded to 6 decimal places is 3.608826.

The cube root of 47 is presented as ∛47 i n the radical form and as (47) ^⅓ or (47)^0.33 in the exponent form. The prime factorization of 47 is 47 itself and this shows that the cube root of 47 when written in its lowest radical form is written as ∛47.

• Cube root of 47: 3.6088
• Cube root of 47 in Exponential Form: (47)^⅓
• Cube root of 47 in Radical Form: ∛47

Note: Cube root of 47 is the real root of the equation x³ = 47.

Value of Cube Root of 47

Exact value of the cube root of 47 is 3.6088 because 3.6088³ ≈ 3.6088 × 3.6088 × 3.6088 ≈ 47

Cube Root of 47 Calculator

Methods to Calculate the Value of the Cube Root of 47

We can calculate cube root of 47 using following two methods:

• Long Division Method
• Halley's Method

Cube Root of 47 By Estimation Method

Use the following steps to find the cube root of 47 by estimation method:

Step 1: Find the nearest perfect cube to 47, which is 27 (3³).

Step 2: Take the difference between 47 and 27, which is 20.

Step 3: Divide 20 by three times the square of the nearest perfect square, which is 3² = 9. This gives us 20/27.

Step 4: Add the result from step 3 to the nearest perfect cube, which is 3. This gives us 3 + 20/27.

This is the estimated value of the cube root of 47 by the estimation method, which is approximately equal to 3.74.

Cube Root of 47 by Halley's Method

Cube root of any number a, can be calculated using the following formula using Halley's Method,

∛a ≈ x - (2x³ - a)/(6x² + 2(a/x))

Where,

• a is the number whose cube root is being calculated, and
• x is the integer guess of its cube root.

For calculation of cube root of 47, a = 47.

Let us assume x as 3. [∵ 3³ is closest to 27 and 27 is the nearest perfect cube that is less than 47]

Therefore,

∛47 ≈ 3 - (2(3)³ - 47)/(6(3)² + 2(47/3)) ≈ 3.74

⇒ ∛47 ≈ 3.74

Therefore, the cube root of 47 is 3.59 approximately.

Is the Cube Root of 47 Irrational?

Yes, the cube root of 47 is irrational. This is because 47 is not a perfect cube; if it were, its cube root would be a whole number, making it a rational number. Instead, the cube root of 47 is approximately 3.609.

Read More,

• Cube Root Calculator
• Cube and Cube Roots
• How to Find the Cube Root of 1000?

Cube Root of 47 Solved Examples

Example 1: Find the real root of the equation x3 − 47 = 0.

Solution:

x³ - 47 = 0 i.e. x³ = 47

Solving for x gives us,

x = ∛47, x = ∛47 × (-1 + √3i))/2 and x = ∛47 × (-1 - √3i))/2

where i is called the imaginary unit and is equal to √-1.

Ignoring imaginary roots,

x = ∛47

Therefore, the real root of the equation x3 - 47 = 0 is for x = ∛47 = 3.6088.

Example 2: The volume of a spherical ball is 47π in³. What is the radius of this ball?

Solution:

= 47π in³

= 4/3 × π × R³

⇒ R³ = 3/4 × 47

⇒ R = ∛(3/4 × 47) = ∛(3/4) × ∛47 = 0.90856 × 3.60883 (∵ ∛(3/4) = 0.90856 and ∛47 = 3.60883)

⇒ R = 3.27884 in³

Example 3: What is the value of ∛47 + ∛(-47)?

Solution:

The cube root of -47 is equal to the negative of the cube root of 47.

i.e. ∛-47 = -∛47

Therefore, ∛47 + ∛(-47) = ∛47 - ∛47 = 0