which is not equal to 3√-125
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Explanation:
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125 is a perfect cube number. 125 can be expressed as a sum of two 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 calculate the square root of 125 by long division method.
Square Root of 125: 5√5
Square of 125: 15,625
Table of Contents
What Is the Square Root of 125?
Is Square Root of 125 Rational or Irrational?
How to Find the Square Root of 125?
Important Notes on Square Root of 125
FAQs on Square Root of 125
Thinking Out of the Box!
Solved Examples on Square Root of 125
Interactive Questions on Square Root of 125
What Is the Square Root of 125?
The square root is an inverse mathematical operation of a square.
The square root of 125 is the value that is obtained after taking the square root of 125.
√125 = 11.1803398875
The simplified radical form of square root of 125 is 5 √5.
Is the Square Root of 125 Rational or Irrational?
It is not possible to find such a whole number which on squaring gives 125
It can be approximately written as a square of 11.180, which is a non-recurring and non-terminating decimal number.
This shows it isn't a perfect square, which also 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. Let us try the prime factorization and the long division method here.
Square Root of 125 by Prime Factorization
To simplify the square root of 125, let us first express 125 as a product of its prime factors.
The prime 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 from the right, we will pair up the digits by putting a bar above them.We will have two pairs, i.e., 1 and 25
Step 2: We divide the left-most number by the largest number whose square is less than or equal to the number in the left-most pair.
Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill the blank which will also 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 remainder.
Step 4: Repeat this process to get the decimal places you want.
finding square root of 125 by long division
Thus √125 = 11.1803398875
Answer:
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