125 is a perfect cube number. 125 have the right to be expressed as a sum of 2 squares in two different ways, 125 = 102 + 52 or 112 + 22. Square Root of 125 is expressed as 5 √5. In this lesboy, we will calculate the square root of 125 by long department technique.

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**Square Root of 125**: 5√5

**Square 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 procedure of a square. The square root of 125 is the worth that is acquired 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 entirety number which on squaring gives 125It deserve to be about 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 type of methods to evaluate the square root of 125. Let us try the prime factorization and the long division strategy right here.

### Square Root of 125 by Prime Factorization

To simplify the square root of 125, let us initially expush 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

**Tip 1:**Starting from the best, we will pair up the digits by placing a bar above them.We will have 2 pairs, i.e., 1 and 25

**Tip 2**: We divide the left-the majority of number by the largest number whose square is much less than or equal to the number in the left-most pair.

**Tip 3**: Double the divisor and also enter it via a empty on its right. Guess the biggest possible digit to fill the blank which will additionally end up being the brand-new digit in the quotient, such that once the new divisor is multiplied to the brand-new quotient the product is much less than or equal to the dividfinish. Divide and also write the remainder.

**Tip 4:**Repeat this process to gain the decimal areas you want.

Hence √125 = 11.1803398875

**Explore Square roots using illustrations and also interenergetic examples**

The prime factorization method is offered to create the square root of a non-perfect square number in the easiest radical develop. For example: 45 = 3 × 3 × 5= 32 × 5.125 is not a perfect square; therefore its square root is an irrational number. This concludes that the square root of any kind of number "n," which is not a perfect square, will certainly constantly be an irrational number.The square root of 125 in the radical create is expressed as 5√5.

How will certainly Sam uncover the square root of 75 and also the square root of 25 using the lengthy division technique up to 3 decimal places?Is √-125 a real number?

**Example 1: **Find the cube root of 125.

**Solution:**

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

Therefore, the cube root of 125 is 5

**Example 2 : **Jack has actually a swimming pool in his home. He finds a square swimming pool that has a room of 125 sq feet. What should be the length of the sides of the square swimming pool?

**Solution:**

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

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