BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation
Login
Creative Math Ideas Image
Live Math Learners Count Icon130 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of 145

Professor Greenline Explaining Math Concepts

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in the field of vehicle design, finance, etc. Here, we will discuss the square root of 145.

Square Root of 145 for Bahraini Students
Professor Greenline from BrightChamps

What is the Square Root of 145?

The square root is the inverse of the square of the number. 145 is not a perfect square. The square root of 145 is expressed in both radical and exponential form. In the radical form, it is expressed as √145, whereas (145)^(1/2) in the exponential form. √145 ≈ 12.0416, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.
square root of 145

Professor Greenline from BrightChamps

Finding the Square Root of 145

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers, where the long division method and approximation method are used. Let us now learn the following methods:

 

  • Prime factorization method
  • Long division method
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 145 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 145 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 145 Breaking it down, we get 5 × 29.

 

Step 2: Now we found out the prime factors of 145. The second step is to make pairs of those prime factors. Since 145 is not a perfect square, the digits of the number can’t be grouped in pairs.

 

Therefore, calculating 145 using prime factorization alone will not give an exact square root.

Professor Greenline from BrightChamps

Square Root of 145 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

 

Step 1: To begin with, we need to group the numbers from right to left. In the case of 145, we need to group it as 45 and 1.

 

Step 2: Now we need to find n whose square is 1. We can say n as ‘1’ because 1×1 is equal to 1. Now the quotient is 1; after subtracting 1-1, the remainder is 0.

 

Step 3: Now let us bring down 45, which is the new dividend. Add the old divisor with the same number 1 + 1, which we get 2 will be our new divisor.

 

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, we need to find the value of n.

 

Step 5: The next step is finding 2n × n ≤ 45. Let us consider n as 2, now 22 = 4 which gives 24 when multiplied by 2, giving 44.

 

Step 6: Subtract 45 from 44, the difference is 1, and the quotient is 12.

 

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 100.

 

Step 8: Now we need to find the new divisor that is 24, because 244 × 4 = 976.

 

Step 9: Subtracting 976 from 1000, we get the result 24.

 

Step 10: Now the quotient is 12.04.

 

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

 

So the square root of √145 is approximately 12.04.

Professor Greenline from BrightChamps

Square Root of 145 by Approximation Method

The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 145 using the approximation method.

 

Step 1: Now we have to find the closest perfect square of √145. The smallest perfect square less than 145 is 144, and the largest perfect square greater than 145 is 169. √145 falls somewhere between 12 and 13.

 

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (145 - 144) ÷ (169 - 144) = 0.04. Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number which is 12 + 0.04 = 12.04.

 

So the square root of 145 is approximately 12.04.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 145

Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting about the negative square root

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one.

For example: √50 ≈ 7.071, there is also -7.071 which should not be forgotten.

Max from BrightChamps Saying "Hey"

Square root of 145 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √145?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The area of the square is approximately 145 square units.

Explanation

The area of the square = side².

The side length is given as √145.

Area of the square = side²

= (√145) × (√145)

= 145.

Therefore, the area of the square box is 145 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped garden measuring 145 square meters is built; if each of the sides is √145, what will be the square meters of half of the garden?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

72.5 square meters

Explanation

We can just divide the given area by 2 as the garden is square-shaped.

Dividing 145 by 2 gives us 72.5.

So half of the garden measures 72.5 square meters.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √145 × 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

60.208

Explanation

The first step is to find the square root of 145, which is approximately 12.0416.

The second step is to multiply 12.0416 by 5.

So 12.0416 × 5 ≈ 60.208.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (145 + 4)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The square root is 13.

Explanation

To find the square root, we need to find the sum of (145 + 4). 145 + 4 = 149, and the closest perfect square is 169.

Therefore, the approximate square root of (145 + 4) is 13.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √145 units and the width ‘w’ is 30 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

We find the perimeter of the rectangle as 84.0832 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√145 + 30)

= 2 × (12.0416 + 30)

= 2 × 42.0416

≈ 84.0832 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 145

1.What is √145 in its simplest form?

Math FAQ Answers Dropdown Arrow

2.Mention the factors of 145.

Math FAQ Answers Dropdown Arrow

3.Calculate the square of 145.

Math FAQ Answers Dropdown Arrow

4.Is 145 a prime number?

Math FAQ Answers Dropdown Arrow

5.145 is divisible by?

Math FAQ Answers Dropdown Arrow

6.How does learning Algebra help students in Bahrain make better decisions in daily life?

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 145?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 145?

Math FAQ Answers Dropdown Arrow

9.Does learning Algebra support future career opportunities for students in Bahrain?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 145

  • Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is √16 = 4.
     
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
     
  • Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is known as the principal square root.
     
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 145 is 5 × 29.
     
  • Long division method: A method used to find the square root of non-perfect squares by systematically dividing the number into parts to approximate the root.
Professor Greenline from BrightChamps

About BrightChamps in Bahrain

At BrightChamps, we understand algebra as more than symbols—it’s a gateway to countless opportunities! We are dedicated to helping children across Bahrain master essential math skills, focusing today on the Square Root of 145 with special attention to square roots—in a fun, lively, and easy-to-follow manner. Whether your child is figuring out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, following local football scores, or managing their allowance to buy the latest gadgets, mastering algebra builds confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Because kids in Bahrain learn differently, we customize our teaching to fit each learner’s style. From Manama’s lively city life to peaceful beaches, BrightChamps brings math to life, making it exciting throughout Bahrain. Let’s make square roots a fun part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom