Square Root

# What Is the Square Root of 125? | How to Find the Square Root of 125?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What Is the Square Root of 125? | How to Find the Square Root of 125?

The square root of 125 is 11.18 mentioned with a symbol √. The square root of 125 is denoted using 125 is or 125^{1/2 }

The square root of a number is determined when a quantity of a number is produced when multiplied by itself or a factor of a number when multiplied by itself gives the original number. In simple terms when a value is multiplied by itself it gives the original number. For a better understanding. The number 5 when multiplied by itself (5 × 5) = 25. The square root for (√25) is 5.

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**Methods to find the square root of 125**

To find the square root of any number first the given number is usually checked to determine whether they are a perfect square number or not. The square of the number s is found using the long division method.

For the number with a perfect square, it is easy to find the square roots and it is a bit tough for non-square values. Numbers like 4,9, 16,25, etc., are perfect squares. Numbers that end with 2,3,7 and 8 are not perfect square numbers.

There are three methods to find the square root of a number

- Prime factorization method
- Long division method
- Repeated subtraction

These methods described above do not apply to finding the square root of any number.

**Prime factorization method**

The prime factors of 125 = 5×5×5

125 = 5×√5

= 5× 2.236

Hence, √125= 11.18

**Long division method**

**Step 1**: Find the smallest integer that can divide the number.**Step 2:**Keep following the long division using divisor and dividend.**Step 3:**When the particular number of satisfaction is reached the quotient is the square root of the number.

**Find the square root of 125**

**Step 1**: Find the smallest integer that can divide the number. 1 is the perfect root number that is smaller and closest to 125.**Step 2:**Keep following the long division using divisor and dividend.

**Step 3**: When the particular number of satisfaction is reached the quotient is the square root of the number.

Hence, the √**125 = 11.180**

**Solved examples**

**Q1: Find the square root of 4 using the prime factorization method**

A1: Prime factors of 4 = 2×2

The √4 = 2

**Q2: What is the square root of 125?**

A2: The √125 = 11.180

**Q3: What is the square root of 49 using repeated division**

- 49-1 = 48
- 48-3 = 45
- 45-5 = 40
- 40-7 = 33
- 33-9 = 24
- 24-11 = 13
- 13-13 = 0

A3: The √49 = 7.

**Q4: What is the square root of 3**

A4: The square root of 3 = 1.7320

**Q5: What is the square root of 5**

A5: The √5 = 2.2360

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**Frequently asked questions**

**What is the √125**?

The √125 = 11.18

**Which method is used to find the √125**?

The standard method that is used to find the square root of any number is the long division method.

**How to write the square root of 125 exponential form?**

125^{1/2} or 125^{0.5 }is the exponential way to write √**125**

**How to write the square root of 125 in radical form?**

The radical form of writing square root i**s √125**

**Can I find the square root of 125 using other methods?**

Prime factor and the long division are used but the long division method is the most widely used method.

**Is 125 an irrational number?**

Yes, 125 is an irrational number since the number is not equal to zero.

**What are the methods to find the square root of a number?**

There are three methods to find the square root of a number

Prime factorization method

Long division method

Repeated subtraction

We hope that we have answered all your queries regarding the square root of 125!

Written by by

Prerit Jain