Square Root Of 125 Simplified

Square Root of 125

125 is a perfect cube number. 125 can exist expressed as a sum of two squares in two different ways, 125 = 10ⁱⁱ + 5^two or 11² + 2². Square Root of 125 is expressed as 5 √5. In this lesson, we volition calculate the foursquare root of 125 by long sectionalization method.

Square Root of 125: v√5
Square of 125: 15,625

What Is the Square Root of 125?

The square root is an inverse mathematical functioning of a foursquare.
The square root of 125 is the value that is obtained after taking the foursquare root of 125.
√125 = eleven.1803398875
The simplified radical class of foursquare root of 125 is five √five.

Is the Foursquare Root of 125 Rational or Irrational?

It is not possible to notice such a whole number which on squaring gives 125
It can be approximately written as a foursquare of xi.180, which is a non-recurring and non-terminating decimal number.
This shows information technology isn't a perfect square, which too proves that the square root of 125 is an irrational number.

How to Find the Square Root of 125?

There are many methods to evaluate the square root of 125. Allow the states try the prime number factorization and the long sectionalisation method here.

Square Root of 125 by Prime Factorization

To simplify the square root of 125, let united states of america beginning express 125 equally a production of its prime number factors.
The prime number factorization of 125 is five × 5 × 5. The square root of 125 is 5 √5.

Square Root of 125 by Long Division Method

Step 1: Starting from the right, we will pair upwards the digits by putting a bar in a higher place them.Nosotros will accept two pairs, i.e., 1 and 25
Pace 2: We divide the left-most number past the largest number whose foursquare is less than or equal to the number in the left-most pair.
Step three: Double the divisor and enter it with a blank on its right. Gauge the largest possible digit to fill the bare which volition likewise become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the residual.
Step 4:Echo this procedure to get the decimal places y'all want.

finding square root of 125 by long division

Thus √125 = 11.1803398875

Explore Square roots using illustrations and interactive examples

Square root of 25
Square root of 85
Square root of 35
Foursquare root of 15
Foursquare root of 169

The prime factorization method is used to write the square root of a non-perfect square number in the simplest radical grade. For example: 45 = 3 × three × 5= 3^two× 5.
125 is not a perfect square; hence its foursquare root is an irrational number. This concludes that the square root of any number "due north," which is non a perfect square, volition always be an irrational number.
The foursquare root of 125 in the radical form is expressed as five√5.

Retrieve Tank:

How will Sam notice the square root of 75 and the foursquare root of 25 using the long division method upwardly to three decimal places?
Is √-125 a existent number?

Case 1:Find the cube root of 125.

Solution:

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

Thus, the cube root of 125 is 5
Example 2 :Jack has a swimming pool in his firm. He finds a foursquare swimming pool that has an expanse of 125 sq feet. What should exist the length of the sides of the square swimming pool?

Solution:

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

Using the property of foursquare roots, √125 = √25 × √5 = five × √five = eleven.18
Hence, the length of the side of the square swimming pool = 11.18 feet.

get to slidego to slide

Breakdown tough concepts through simple visuals.

Math volition no longer exist a tough subject area, especially when y'all understand the concepts through visualizations.

Book a Free Trial Class

go to slidego to slidego to slide

FAQs On Square Root of 125

What is the foursquare root of 125?

The square root of 125 is xi.180.

Is 125 a cube number?

Yes, 125 is a cube number of the whole number 5. (125 = 5 × v × 5 )

What is the square root of 125 simplified?

The square root of 125 in the simplest class is 5 √5.

Is square root of 125 a real number?

Yes, square root of 125 is a real number.

What is a square of 125?

125 × 125 = 15,625