Cube Root of 25

The cube root of 25 is a real number whose cube is 25. Let x be the cube root of 25, then ∛25 = x and x³ = 25. The sign “√” is called the radical sign, often used to represent the nth root of a number and “∛” is used to represent the cube root of a number.

The cube root of 25 in exponential form is written as 25^1/3. Let us learn how to find the cube root of 25.

What is the Cube Root of 25?

The cube root of 25 is the number whose cube is 25. A perfect cube is a number which is the cube of an integer. Since we cannot find any integer whose cube is 25, therefore 25 is not a perfect cube number. Learn the cube root of 25 and also learn how to calculate the cube root of 25.

Check the cubes of numbers from 1 to 50.

How to Find the Cube Root of 25?

The cube root of 25 is not a rational number as we cannot find any integer whose cube is 25. Thus we cannot use the prime factorisation method to find the cube root of 25. To calculate the cube root of 25, we are going to Halley’s method, whose formula is given by:

Halley Formula for Cube Root:

Where a = the number whose cube root is to be determined.

x = is the guess number which is the cube root of the nearest perfect cube.

Now, let us calculate the cube root of 25 by Halley’s method. Here a = 25 and 2³ = 8 < 25 we take x = 2. Let us put these values in the above formula, we get

∛25 = 2[(2³ + 2 × 25)/(2 × 2³ + 25)]

= 2[(8 + 50)/(16 + 25)]

= 2[(58)/(41)] ≈ 2.83.

Hence, the cube root of 25 using Halley’s method is 2.83 (approx)

Video Lesson on Finding Cube Roots

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Solved Examples on Cube Root of 25

Example 1:

What is the smallest number that must be multiplied by 25 to make it a perfect cube number?

Solution:

The prime factorisation of 25 = 5 × 5

To find the cube root of 25, we need to make a group of 3 for each factor. Therefore, we must multiply 25 by 5 to get a perfect cube number.

25 × 5 = 125 is a perfect cube number.

The cube root of 125 = ∛(5 × 5 × 5) = 5.

Example 2:

Find the length of the side of the cube whose volume is 25 cm³.

Solution:

Let x be the side of the cube.

The volume of the cube = x³ = 25 cm³

⇒ x = ∛25 = 2.9 cm (approx.)

Example 3:

Find the length of the radius of a cone whose height is equal to three times its base radius and volume is 25𝜋 cm³.

Solution:

Let r be the base radius of the cone.

The height of the cone is 3r.

The volume of the cone = ⅓ 𝜋 r² 3r = 25𝜋

⇒ r³ = 25

⇒ r = ∛25 = 2.9 cm (approx.)

∴ the length of the radius of cone is 2.9 cm.