127 LearnersLast updated on May 26th, 2025
Square Root of 667
If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 667.
What is the Square Root of 667?
The square root is the inverse of the square of the number. 667 is not a perfect square. The square root of 667 is expressed in both radical and exponential form. In the radical form, it is expressed as √667, whereas in exponential form it is expressed as (667)^(1/2). √667 ≈ 25.81989, 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.
Finding the Square Root of 667
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long division and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 667 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 667 is broken down into its prime factors.
Step 1: Finding the prime factors of 667 667 is a prime number itself. Therefore, we cannot break it down further into other prime factors.
Since 667 is not a perfect square, calculating 667 using prime factorization is not feasible for finding its square root.
Square Root of 667 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 667, we need to group it as 67 and 6.
Step 2: Now we need to find n whose square is 6. We can say n as ‘2’ because 2x2 is lesser than or equal to 6. Now the quotient is 2 and after subtracting 6-4 the remainder is 2.
Step 3: Now let us bring down 67 which is the new dividend. Add the old divisor with the same number 2 + 2 we get 4 which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 4n x n ≤ 267. Let us consider n as 6, now 46x6 = 276, which is larger, so let’s try n as 5, now 45x5 = 225.
Step 6: Subtract 267 from 225, the difference is 42, and the quotient is 25.
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 4200.
Step 8: Now we need to find the new divisor that is 519 because 519x8 = 4152.
Step 9: Subtracting 4152 from 4200 we get the result 48.
Step 10: Now the quotient is 25.8.
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 √667 is approximately 25.82.
Square Root of 667 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 667 using the approximation method.
Step 1: Now we have to find the closest perfect square to √667. The smallest perfect square less than 667 is 625, and the largest perfect square greater than 667 is 676. √667 falls somewhere between 25 and 26.
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 (667 - 625) / (676 - 625) = 42/51 ≈ 0.8235 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 25 + 0.82 ≈ 25.82, so the square root of 667 is approximately 25.82.
Common Mistakes and How to Avoid Them in the Square Root of 667
Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
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: √667 ≈ 25.82, there is also -25.82 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root symbol properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For Example: √(36+49) ≠ √36 + √49. The right way of using roots is √(36+49) = √85.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For Example: √50 ≈ 7.07, not √50 = 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the cube root and the square root constantly, as this will help them keep away from mistakes.
For Example: √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 667 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √667?
The area of the square is approximately 445.31 square units.
Explanation
The area of the square = side².
The side length is given as √667.
Area of the square = side² = √667 x √667 ≈ 25.82 x 25.82 ≈ 445.31.
Therefore, the area of the square box is approximately 445.31 square units.
Problem 2
A square-shaped building measuring 667 square feet is built; if each of the sides is √667, what will be the square feet of half of the building?
333.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 667 by 2 = we get 333.5.
So half of the building measures 333.5 square feet.
Problem 3
Calculate √667 x 5.
129.1
Explanation
The first step is to find the square root of 667, which is approximately 25.82.
The second step is to multiply 25.82 with 5.
So 25.82 x 5 ≈ 129.1.
Problem 4
What will be the square root of (667 + 9)?
The square root is 26.
Explanation
To find the square root, we need to find the sum of (667 + 9).
667 + 9 = 676, and then √676 = 26.
Therefore, the square root of (667 + 9) is ±26.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √667 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 127.64 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√667 + 38)
≈ 2 × (25.82 + 38)
≈ 2 × 63.82
≈ 127.64 units.
FAQ on Square Root of 667
1.What is √667 in its simplest form?
2.Mention the factors of 667.
3.Calculate the square of 667.
4.Is 667 a prime number?
5.667 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 667?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 667?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 667
- Square root: A square root is the inverse of a square. Example: 5² = 25 and the inverse of the square is the square root, that is √25 = 5.
- 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.
- Prime number: A prime number is a number greater than 1 with no divisors other than 1 and itself.
- Long division method: A method used to find the square root of a number, especially when the number is not a perfect square.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
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About BrightChamps in Saudi Arabia
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.
