# Cube root of 125

The cube root of 125 is a number when multiplied by itself two times will be 125. If a cube has a volume of 125 unit3, then we use the value of the cube root of 125 to find the length of the cube.

The cube root of 125 is denoted by the symbol $\sqrt{125}$. In this section, we will learn how to find the value of $\sqrt{125}$.

The value of the cube root of 125 is 5.

#### Important Things:

• $\sqrt{125} = 5$
• 125 is a perfect cube.
• $\sqrt{125}$ is the surd form of cube root of 125.
• 1251/3is the exponential form of cube root of 125.
• The cube root of 125 is 5.000 in decimal form.
• cube of 125: 125×125×125 = 1953125

Let us now calculate the cube root of 125.

#### What is the Cube Root of 125?

We know that 125=5×5×5. As this is a product of three number of 5‘s. we can write

125=53

Taking cube root on both sides, we have

$\sqrt{125} = \sqrt{5^3}$

As cube root can be written as power 1/3, we get that

$\sqrt{125}$ = (53)1/3

= 51/3   as we know that (am)n = am×n

= 5= 5

So the cube root of 125 is 5.

#### Is 125 a perfect cube number?

We have calculated above that $\sqrt{125}=5$. As 5 is a whole number, the cube root of 125 is also a whole number. So by the definition of a perfect cube, we conclude that 125 is a perfect cube number.

#### Cube root of 125 by Prime Factorization

Note that the value of the cube root of 125 is 5. To prove this by the prime factorization method, we will at first factorize 125.

As 125 has the unit digit 5, it will be divisible by 5. So we have

125=5×25

By the above logic, we write

25=5×5.

So finally we get

125=5×5×5 …(∗)

Note that the above is the prime factorization of 125.

Taking cube root on both sides of (∗), we get that

$\sqrt{125} = \sqrt{5×5×5}$

= 5 as we know that $\sqrt{a×a×a}=a$

∴  the cube root of 125 is 5

#### Is Cube Root of 125 Rational?

By definition, we know that a rational number can be expressed as p/q where p and q are integers with q ≠ 0.

We have found above that $\sqrt{125}=5$.

Note that 5=5/1.

So 5 can be written as p/q with p=5, q=1≠0.

5 is a rational number.

⇒ the cube root of 125 is also a rational number.

Conclusion: The cube root of 125 is not an irrational number.