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Last updated on May 26th, 2025

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Square Root of 167

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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.

Square Root of 167 for US Students
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.

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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.

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

Errors can occur while calculating square roots, such as ignoring the negative root or misapplying methods. Let's examine some common mistakes:

Mistake 1

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Forgetting about the negative square root

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Students should remember that a number has both positive and negative square roots. Typically, we only use the positive square root, but the negative is equally valid.

For example, √50 = ±7.07.

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Square Root of 167 Examples

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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?

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The area of the square is approximately 167 square units.

Explanation

The area of the square = side^2.

The side length is given as √167.

Area of the square = (√167)^2

= 167.

Therefore, the area of the square box is approximately 167 square units.

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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?

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83.5 square feet

Explanation

Since the garden is square-shaped, dividing the total area by 2 gives the area of half the garden.

167 / 2 = 83.5

So, half of the garden measures 83.5 square feet.

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Problem 3

Calculate √167 × 4.

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Approximately 51.69

Explanation

First, find the square root of 167, which is approximately 12.9228. Multiply this by 4. 12.9228 × 4 ≈ 51.69

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Max, the Girl Character from BrightChamps

Problem 4

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

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The square root is 13.

Explanation

Calculate the sum inside the parentheses: 149 + 18 = 167.

The square root of 167 is approximately 12.9228, which rounds to 13.

Therefore, the square root of (149 + 18) is approximately 13.

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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.

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The perimeter of the rectangle is approximately 105.85 units.

Explanation

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

Perimeter = 2 × (√167 + 40)

= 2 × (12.9228 + 40)

≈ 105.85 units.

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FAQ on Square Root of 167

1.What is √167 in its simplest form?

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2.Mention the factors of 167.

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3.Calculate the square of 167.

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4.Is 167 a prime number?

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5.167 is divisible by?

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

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7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 167?

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8.How do technology and digital tools in United States support learning Algebra and Square Root of 167?

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

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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.
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we understand algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to empower kids throughout the United States to master key math skills, like today’s topic on the Square Root of 167, with a special emphasis on understanding square roots—in an engaging, fun, and easy-to-grasp manner. Whether your child is calculating how fast a roller coaster zooms through Disney World, keeping track of scores during a Little League game, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence to tackle everyday problems. Our hands-on lessons make learning both accessible and exciting. Since kids in the USA learn in diverse ways, we customize our methods to suit each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps brings math alive, making it meaningful and enjoyable all across America. Let’s make square roots an exciting part of every child’s math adventure!
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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.

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Fun Fact

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

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