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 together 5 √5. In this lesson, we will calculate the square source of 125 by long department method.

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**Square root of 125**: 5√5

**Square that 125:**15,625

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

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

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

4. | FAQs top top Square root of 125 |

## What Is the Square root of 125?

The square root is an station mathematical operation of a square. The square source of 125 is the worth that is derived after acquisition the square root of 125. √125 = 11.1803398875The streamlined radical type of square source of 125 is 5 √5.It is not feasible to discover such a whole number which on squaring gives 125It can be around written as a square of 11.180, i beg your pardon is a non-recurring and also non-terminating decimal number.This mirrors it isn"t a perfect square, which additionally proves that

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

## How to discover the Square root of 125?

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

### Square root of 125 by prime Factorization

To leveling the square root of 125, permit us first express 125 as a product the its prime factors. The element 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 native the right, we will pair up the number by putting 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 whose square is much less than or equal to the number in the left-most pair.

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

**Step 4:**Repeat this procedure to gain the decimal places you want.

Thus √125 = 11.1803398875

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

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

Thus, the cube source of 125 is 5

**Example 2 : **Jack has actually a swimming swimming pool in his house. That finds a square swim pool that has an area the 125 sq feet. What must be the length of the sides of the square swim pool?

**Solution:**

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

See more: How Many Diagonals Does A Heptagon Have, Diagonals Of Heptagons

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