125 is a perfect cube number. 125 deserve to be expressed as a amount of two squares in two various ways, 125 = 102 + 52 or 112 + 22. Square root of 125 is expressed as 5 √5. In this lesson, we will certainly calculate the square root of 125 by 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 source of 125 reasonable or Irrational? |

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

4. | FAQs on Square source of 125 |

## What Is the Square source of 125?

The square source is an train station mathematical procedure of a square. The square source of 125 is the worth that is acquired after taking the square source of 125. √125 = 11.1803398875The simplified radical type of square source of 125 is 5 √5.It is not possible to find such a whole number which on squaring offers 125It have the right to be approximately written as a square the 11.180, i m sorry is a non-recurring and non-terminating decimal number.This mirrors it isn"t a perfect square, which also proves that

**the square root of 125 is one irrational number.**

## How to discover the Square root of 125?

There are many methods to advice the square root of 125. Allow us shot the prime factorization and the long division method here.

### Square source of 125 by prime Factorization

To simplify the square root of 125, permit us an initial express 125 as a product that its prime factors. The element factorization of 125 is 5 × 5 × 5. The square root of 125 is 5 √5.

### Square source of 125 by Long department Method

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

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

**Step 3**: double the divisor and also enter it with a blank on that right. Guess the largest possible digit to fill the blank which will also become the brand-new digit in the quotient, together that once the new divisor is multiply to the brand-new quotient the product is much less than or same to the dividend. Divide and also write the remainder.

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

Thus √125 = 11.1803398875

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

The prime factorization technique is offered to write the square root of a non-perfect square number in the most basic radical form. Because that example: 45 = 3 × 3 × 5= 32 × 5.125 is no a perfect square; hence its square source is an irrational number. This concludes the the square source of any type of number "n," which is not a perfect square, will constantly be an irrational number.The square root of 125 in the radical type is expressed as 5√5.

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

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

**Solution:**

A** **cube source 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 actually an area the 125 sq feet. What need to be the size of the sides of the square swimming pool?

**Solution:**

The area of the square swimming pool is 125 square feet.The size of every side that the swim pool is the square source of its area.

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