BrightChamps Logo
Hamburger Menu Icon for BrightChamps Website Navigation

Math Table of Contents Dropdown Table Of Contents

Creative Math Ideas Image
Live Math Learners Count Icon102 Learners

Last updated on April 28th, 2025

Math Whiteboard Illustration

Square Root of 167

Professor Greenline Explaining Math Concepts
Foundation
Intermediate
Advance Topics

If a number is multiplied by itself, the result is a square. The inverse operation is finding the square root. The square root has applications in various fields such as engineering, physics, and finance. Here, we will discuss the square root of 167.

Professor Greenline from BrightChamps

What is the Square Root of 167?

The square root is the inverse operation of squaring a number. 167 is not a perfect square. The square root of 167 can be expressed in both radical and exponential forms. In the radical form, it is expressed as √167, whereas in the exponential form, it is expressed as (167(1/2) .The approximate value of √167 is 12.9228, which is an irrational number because it cannot be expressed as a fraction of two integers.
square root of 167

Professor Greenline from BrightChamps

Finding the Square Root of 167

For perfect square numbers, the prime factorization method is effective. However, for non-perfect squares like 167, the long division method and approximation method are more suitable. Let's explore these methods:

 

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

Square Root of 167 by Prime Factorization Method

Prime factorization involves expressing a number as a product of prime numbers.

For 167, the prime factorization is straightforward since 167 is a prime number itself. Thus, it cannot be factored further.

Since 167 is not a perfect square, we cannot pair its prime factors to simplify the square root. Therefore, calculating √167 using prime factorization is not feasible.

Professor Greenline from BrightChamps

Square Root of 167 by Long Division Method

The long division method is used for finding the square roots of non-perfect square numbers. Here’s how it works for 167:

 

Step 1: Group the number from right to left. In the case of 167, we group it as (1)(67).

 

Step 2: Find a number n whose square is less than or equal to 1. Here, n is 1 since 1^2 = 1. The quotient becomes 1, and the remainder is 0.

 

Step 3: Bring down the next group, 67, making the new dividend 67. Add the previous divisor (1) to itself to get 2, which is part of the new divisor.

 

Step 4: Consider 2n as the new divisor. We need to find n such that 2n × n ≤ 67. Trying n as 3 gives 23 × 3 = 69, which is too large. Trying n as 2 gives 22 × 2 = 44, which fits.

 

Step 5: Subtract 44 from 67 to get a remainder of 23.

 

Step 6: Since the new dividend is smaller than the divisor, add a decimal point and bring down two zeros to make it 2300.

 

Step 7: Find the new divisor, which becomes 249 (since the previous quotient was 12). Find n such that 249n × n ≤ 2300. Trying n as 9 gives 2499 × 9 = 2241.

 

Step 8: Subtract 2241 from 2300 to get a remainder of 59.

 

Step 9: Continue this process to get more decimal places as needed.

 

Thus, √167 ≈ 12.9228.

Professor Greenline from BrightChamps

Square Root of 167 by Approximation Method

Approximation is a simpler method to estimate square roots. Follow these steps for √167:

 

Step 1: Identify the closest perfect squares. 144 and 169 are the nearest perfect squares to 167. √167 lies between √144 (12) and √169 (13).

 

Step 2: Use the formula to approximate: (Given number - smaller perfect square) / (Greater perfect square - smaller perfect square). For 167, (167 - 144) / (169 - 144) = 23 / 25 = 0.92. Step 3: Add the approximation to the smaller square root value: 12 + 0.92 = 12.92.

 

Therefore, √167 is approximately 12.92.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 167

Max from BrightChamps Saying "Hey"

Square Root of 167 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 √167?

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

Explanation

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

Problem 2

A square-shaped garden measuring 167 square feet is being designed; if each side is √167, what will be the square feet of half of the garden?

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

Explanation

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

Problem 3

Calculate √167 × 4.

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

Explanation

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

Problem 4

What is the square root of (149 + 18)?

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

Explanation

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

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √167 units and the width ‘w’ is 40 units.

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

Explanation

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

FAQ on Square Root of 167

1.What is √167 in its simplest form?

Math FAQ Answers Dropdown Arrow

2.Mention the factors of 167.

Math FAQ Answers Dropdown Arrow

3.Calculate the square of 167.

Math FAQ Answers Dropdown Arrow

4.Is 167 a prime number?

Math FAQ Answers Dropdown Arrow

5.167 is divisible by?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 167

  • Square root: The number that, when multiplied by itself, gives the original number. Example: √16 = 4 because 4 × 4 = 16.
     
  • Irrational number: A number that cannot be expressed as a simple fraction, with a non-repeating and non-terminating decimal. Example: √2.
     
  • Prime number: A natural number greater than 1 that has no positive divisors other than 1 and itself. Example: 167.
     
  • Approximation: The process of finding a value that is close to but not exactly equal to a specific number.
     
  • Perfect square: A number that is the square of an integer. Example: 144, as 12 × 12 = 144.
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.

BrightChamps Logo
Follow Us
BrightChamps Facebook Page IconBrightChamps YouTube Channel IconBrightChamps Instagram IconBrightChamps LinkedIn Page Icon
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