125 is a perfect cube number. 125 can be expressed together a amount of 2 squares in two different 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 department method.

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Square source of 125: 5√5Square of 125: 15,625
 1 What Is the Square root of 125? 2 Is Square root of 125 rational or Irrational? 3 How to discover the Square root of 125? 4 FAQs top top Square source of 125

## What Is the Square root of 125?

The square source is an inverse mathematical operation of a square. The square source of 125 is the value that is obtained after acquisition the square source of 125.  √125 = 11.1803398875The simplified radical type of square root of 125 is 5 √5.
It is not feasible to find such a entirety number which ~ above squaring provides 125It deserve to be roughly written as a square that 11.180, which is a non-recurring and non-terminating decimal number.This reflects it isn"t a perfect square, which also proves the the square root of 125 is an irrational number.

## How to uncover the Square source of 125?

There are many methods to evaluate the square source of 125. Allow us shot the prime 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 that its element 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 from the right, we will certainly pair increase the digits by putting a bar over them.We will have actually two pairs, i.e., 1 and 25Step 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: twin the divisor and also enter it with a empty on its right. Guess: v the largest possible digit to to fill the blank which will additionally become the 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 equal to the dividend. Divide and also write the remainder. Step 4: Repeat this process to obtain the decimal locations you want. Thus √125 = 11.1803398875

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The prime factorization method is supplied to create the square root of a non-perfect square number in the easiest radical form. Because that example: 45 = 3 × 3 × 5= 32 × 5.125 is no a perfect square; hence that square source is an irrational number. This concludes that the square root of any type of number "n," which is no a perfect square, will always be one irrational number.The square root of 125 in the radical type is expressed together 5√5.
How will certainly Sam find the square root of 75 and also the square source of 25 using the long department method approximately 3 decimal places?Is √-125 a actual number?

Example 1: Find the cube root of 125.

Solution:

A cube source 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 a swimming pool in his house. That finds a square swim pool that has an area that 125 sq feet. What should be the size of the sides the the square swimming pool?

Solution:

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

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