125 is a perfect cube number. 125 can be expressed as a sum of two squares in two different ways, 125 = 102 + 52 or 112 + 22. Square Root of 125 is expressed as 5 √5. In this lesson, we will calculate the square root of 125 by long division method.

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Square Root of 125: 5√5Square of 125: 15,625
1.What Is the Square Root of 125?
2.Is Square Root of 125 Rational or Irrational?
3.How to Find the Square Root of 125?
4.FAQs on Square Root of 125

What Is the Square Root of 125?

The square root is an inverse mathematical operation of a square. The square root of 125 is the value that is obtained after taking the square root of 125.  √125 = 11.1803398875The simplified radical form of square root of 125 is 5 √5.
It is not possible to find such a whole number which on squaring gives 125It can be approximately written as a square of 11.180, which is a non-recurring and non-terminating decimal number.This shows it isn"t a perfect square, which also proves that the square root of 125 is an irrational number.

How to Find the Square Root of 125?

There are many methods to evaluate the square root of 125. Let us try the prime factorization and the long division method here. 

Square Root of 125 by Prime Factorization

To simplify the square root of 125, let us first express 125 as a product of its prime factors. The prime factorization of 125 is 5 × 5 × 5. The square root of 125 is 5 √5.

Square Root of 125 by Long Division Method

Step 1: Starting from the right, we will pair up the digits by putting a bar above them.We will have two pairs, i.e., 1 and 25Step 2: We divide the left-most number by the largest number whose square is less than or equal to the number in the left-most pair.Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder. Step 4: Repeat this process to get the decimal places you want.


 Thus √125 = 11.1803398875

Explore Square roots using illustrations and interactive examples

The prime factorization method is used to write the square root of a non-perfect square number in the simplest radical form. For example: 45 = 3 × 3 × 5= 32 × 5.125 is not a perfect square; hence its square root is an irrational number. This concludes that the square root of any number "n," which is not a perfect square, will always be an irrational number.The square root of 125 in the radical form is expressed as 5√5.
How will Sam find the square root of 75 and the square root of 25 using the long division method up to 3 decimal places?Is √-125 a real number?

Example 1: Find the cube root of 125.


A cube root of a number is expressed as number × number × number.125 = 5 × 5 × 5

Thus, the cube root of 125 is 5

Example 2 : Jack has a swimming pool in his house. He finds a square swimming pool that has an area of 125 sq feet. What should be the length of the sides of the square swimming pool?


The area of the square swimming pool is 125 square feet.The length of each side of the swimming pool is the square root of its area.

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Using the property of square roots, √125 = √25 × √5 = 5 × √5 = 11.18Hence, the length of the side of the square swimming pool = 11.18 feet.