107 LearnersLast updated on May 26th, 2025
Square Root of 139.25
If a number is multiplied by itself, the result is a square. The inverse of this process is finding the square root. Square roots are used in various fields such as engineering, finance, and physics. Here, we will discuss the square root of 139.25.
What is the Square Root of 139.25?
The square root is the inverse operation of squaring a number. 139.25 is not a perfect square. The square root of 139.25 can be expressed in both radical and exponential forms. In radical form, it is expressed as √139.25, whereas in exponential form it is (139.25)(1/2). The square root of 139.25 is approximately 11.799, which is an irrational number because it cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 139.25
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods such as the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 139.25 by Long Division Method
The long division method is particularly useful for non-perfect square numbers. Here is how to find the square root using the long division method, step by step:
Step 1: Group the digits of 139.25 from right to left into pairs: 39|25.
Step 2: Find a number whose square is less than or equal to 39. The number is 6 (since 6 x 6 = 36).
Step 3: Subtract 36 from 39, and bring down 25 to get 325.
Step 4: Double the divisor (6) to get 12. Now find a digit n such that 12n * n is close to 325. The digit n is 2 (since 122 x 2 = 244).
Step 5: Subtract 244 from 325 to get 81.
Step 6: Add a decimal point to the quotient, and bring down 00 to get 8100.
Step 7: The new divisor is 124. Find a digit n such that 124n * n is close to 8100. The digit n is 6 (since 1246 x 6 = 7476).
Step 8: Subtract 7476 from 8100 to get 624.
Step 9: Continue the process to get more decimal places.
So, the square root of 139.25 is approximately 11.799.
Square Root of 139.25 by Approximation Method
The approximation method is a simpler way to find the square root of a number:
Step 1: Identify the two perfect squares between which 139.25 lies. The closest perfect squares are 121 (112) and 144 (122).
Step 2: √139.25 lies between 11 and 12.
Step 3: Use interpolation to estimate: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square) = (139.25 - 121) / (144 - 121)
This results in approximately 0.799. Adding the initial whole number 11 to the decimal point, we get 11 + 0.799 = 11.799.
So, the approximate square root of 139.25 is 11.799.
Common Mistakes and How to Avoid Them in the Square Root of 139.25
Students often make mistakes while finding square roots, such as ignoring the negative square root or skipping steps in the long division method. Here are a few common mistakes students make:
Mistake 1
Forgetting about the negative square root
It's important for students to know that a number has both positive and negative square roots. However, we usually consider only the positive square root.
For example, √50 = 7.07, but it also has a negative counterpart, -7.07.
Square root of 139.25 Examples
Problem 1
Can you help Max find the area of a square if its side length is given as √139?
The area of the square is approximately 139 square units.
Explanation
The area of a square = side^2.
Given the side length as √139, Area = (√139) × (√139) = 139.
Therefore, the area of the square is approximately 139 square units.
Problem 2
A square-shaped garden measures 139.25 square meters in area. If each side is √139.25 meters, what is the area of half of the garden?
69.625 square meters
Explanation
To find the area of half the garden, divide the total area by 2: 139.25 / 2 = 69.625 square meters.
So, half of the garden measures 69.625 square meters.
Problem 3
Calculate √139.25 × 4.
47.196
Explanation
First, find the square root of 139.25, which is approximately 11.799.
Then multiply by 4: 11.799 × 4 = 47.196.
So, √139.25 × 4 = 47.196.
Problem 4
What will be the square root of (140 + 5)?
The square root is 12.
Explanation
First, find the sum of (140 + 5): 140 + 5 = 145
The square root of 145 is approximately 12.042, but rounding to the nearest whole number gives 12.
Therefore, the square root of (140 + 5) is approximately ±12.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √139 units and the width ‘w’ is 39 units.
The perimeter of the rectangle is approximately 101.598 units.
Explanation
Perimeter of a rectangle = 2 × (length + width).
Perimeter = 2 × (√139 + 39)
≈ 2 × (11.789 + 39)
≈ 2 × 50.789
= 101.598 units.
FAQ on Square Root of 139.25
1.What is √139.25 in its simplest form?
2.Mention the factors of 139.25.
3.Calculate the square of 139.25.
4.Is 139.25 a prime number?
5.139.25 is divisible by?
Important Glossaries for the Square Root of 139.25
- Square root: The square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the square root is √16 = 4.
- Irrational number: An irrational number cannot be expressed as a fraction p/q, where p and q are integers with q ≠ 0. The square root of most non-perfect squares is irrational.
- Decimal: A decimal number includes a whole number and a fractional part separated by a decimal point, such as 7.86 or 11.799.
- Long Division Method: A step-by-step process to find square roots of non-perfect square numbers by grouping, dividing, and subtracting.
- Perfect Square: A perfect square is an integer that is the square of another integer. For example, 144 is a perfect square because it is 12^2.
Explore More algebra
Previous to Square Root of 139.25
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
