125 is a perfect cube number. 125 deserve to be expressed together a amount of 2 squares in two various ways, 125 = 102 + 52 or 112 + 22. Square source of 125 is expressed as 5 √5. In this lesson, we will calculate the square root of 125 through long division method.

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**Square source of 125**: 5√5

**Square the 125:**15,625

1. | What Is the Square source of 125? |

2. | Is Square root of 125 reasonable or Irrational? |

3. | How to uncover the Square root of 125? |

4. | FAQs ~ above Square source of 125 |

## What Is the Square source of 125?

The square source is an inverse mathematical procedure of a square. The square source of 125 is the value that is derived after acquisition the square root of 125. √125 = 11.1803398875The simplified radical type of square source of 125 is 5 √5.It is not possible to discover such a whole number which ~ above squaring provides 125It have the right to be approximately written as a square the 11.180, i beg your pardon is a non-recurring and non-terminating decimal number.This reflects it isn"t a perfect square, which also proves that

**the square source of 125 is an irrational number.**

## How to uncover the Square root of 125?

There are countless methods to evaluate the square source of 125. Allow us shot the element factorization and also the long department method here.

### Square source of 125 by prime Factorization

To leveling the square source of 125, permit us first express 125 as a product the its prime factors. The prime factorization of 125 is 5 × 5 × 5. The square source of 125 is 5 √5.

### Square root of 125 by Long department Method

**Step 1:**Starting native the right, we will pair increase the number by placing a bar above them.We will have two pairs, i.e., 1 and 25

**Step 2**: We division the left-most number through the biggest number who square is less than or same to the number in the left-most pair.

**Step 3**: twin the divisor and enter it through a blank on that right. Guess the largest feasible digit to fill the blank which will additionally become the brand-new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or same to the dividend. Divide and write the remainder.

**Step 4:**Repeat this process to acquire the decimal places you want.

Thus √125 = 11.1803398875

**Explore Square roots utilizing illustrations and also interactive examples**

The prime factorization technique is provided to compose the square source of a non-perfect square number in the easiest radical form. Because that example: 45 = 3 × 3 × 5= 32 × 5.125 is not a perfect square; hence its square root is one irrational number. This concludes the the square root of any kind of number "n," which is no a perfect square, will always be an irrational number.The square root of 125 in the radical type is expressed together 5√5.

How will Sam find the square source of 75 and the square source of 25 utilizing the long department method approximately 3 decimal places?Is √-125 a genuine number?

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

**Solution:**

A** **cube root of a number is expressed together 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. That finds a square swim pool that has actually an area the 125 sq feet. What need to be the length of the sides that the square swimming pool?

**Solution:**

The area the the square swimming pool is 125 square feet.The size of each side that the swimming pool is the square source of that is area.

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Using the building of square roots, √125 = √25 × √5 = 5 × √5 = 11.18Hence, the size of the next of the square swimming swimming pool = 11.18 feet.