Cube Root of 125

Cube root of 125 is 5. Cube root of 125 is represented as, (125)^1/3 and in radical form ∛(125)​. In this article, we will learn about, Cube Root of 125, Root of 125 using different methods, such as Prime Factorization Methods and others in detail.

👁 Cube-Root-of-125

What is Cube Root of 125?

Cube root of 125 is a number that, when multiplied by itself three times, gives the original number 125. As mentioned above, the cube root 125 is denoted by the symbol ∛125​ or (125)^1/3. To find value of cube root of 125, we use different methods, such as prime factorization and division method.

• Cube Root of 125: 5
• Cube Root of 125 in Exponential Form: (125)^1/3
• Cube Root of 125 in Radical Form: ∛(125)

These methods are discussed in the next section in detail. Before moving forward we must learn about cube root in brief.

Cube Root Definition

Cube root of a number a is a number x such that x³ = a, in other words, a number x whose cube is . For example, 5 is the cube root of 125 because 5³ = 5×5×5 = 125, and −5 is cube root of −125 because (−5)³ = (−5) × (−5) × (−5) = −125.

Cube root of a number a is denoted by the symbol ∛a​ or (a)^1/3. For example, cube root 125 is written as ∛125​ or (125)^1/3.

Value of Cube Root of 125

Value of cube root of 125 is 5 since, cube of number 5 equals 125. That is, ∛125 ​= ∛(5×5×5) ​= 5. We can also verify this value by using a calculator or by raising both sides of the equation to the power of 3.

For example,

(∛125​)³ = 125

Cube Root of 125 Calculator

How to Calculate Value of Cube Root of 125?

There are different methods to calculate the value of cube root of any number, such as Cube Root of 125 by Prime Factorization,

Cube Root of 125 by Prime Factorization

Prime factorization is a method of expressing a number as a product of its prime factors. Prime factors are the numbers that are divisible only by 1 and themselves, such as 2, 3, 5, 7, etc.

👁 Prime-Factors-of-125

To find cube root of 125 by prime factorization, we need to follow these steps:

Step 1: Find prime factors of 125 by dividing it by the smallest prime number until we get 1 as the quotient.

125 ÷ 5 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

Step 2: Write prime factors of 125 as a product.

125 = 5×5×5

Step 3: Group prime factors of 125 in set of three and write them in form of cubes.

125 = (5×5×5) = 5³

Step 4: Apply cube root on both sides of equation to cancel cube of number.

∛(125) ​ = ∛(5³)

Step 5: Simplify cube root by taking out common factor from each group.

∛125 ​= ∛5³ = 5

Therefore, cube root of 125 by prime factorization is 5.

Cube Root of Numbers

Table added below shows the cube root of first 1 to 10 perfect cube,

Number (n)	Cube Root of a Number (∛n)
1	1
8	2
125	3
64	4
125	5
216	6
343	7
512	8
729	9
1000	10

Learn more, Cube Root 1 to 30

Is Cube Root of 125 Irrational?

No, cube root of 125 is not irrational. An irrational number is a number that cannot be expressed as a ratio of two integers, such as √2​, π, e, etc. Cube root of 125 is equal to 5, which is an integer. Therefore, it can be expressed as a ratio of two integers, such as 5/1, 10/2, 15/3, etc. Therefore, cube root of 125 is a rational number.

Read More,

• Cubes and Cube Roots

Cube Root of 125 - Solved Examples

Here are some solved examples of problems involving the cube root of 125.

Example 1: Find value of ∛(125) ​+ ∛(−125)​.

Solution:

Cube root of (−125) = -5

Cube root of (125) = 5

Therefore,

∛(125)​ + ∛(−125)​

= ∛125​ - ∛125 ​

= 5 − 5 = 0

Example 2: Given volume of a cube is 125 cm³. Find length of side of cube.

Solution:

Volume of a cube (V) = a³, where a is length of side of cube

To find length of side of cube, we need to find cube root of volume

a = (V)^1/3​

Substituting value of V = 125 cm³

a = ∛(125)

a = 5 cm

Therefore, length of side of cube is 5 cm

Example 3: Find real root of equation x³ − 125 = 0.

Solution:

To find real root of equation, we need to isolate x by adding 125 to both sides of equation.

x³ = 125

Then, we need to take cube root of both sides of equation to cancel cube of x

x = ∛(125)​

Since, cube root of 125 is 5

x = 5

Therefore,

Real root of equation x³ − 125 = 0 is x = 5