117 LearnersLast updated on May 26th, 2025
Square Root of 2669
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 2669.
What is the Square Root of 2669?
The square root is the inverse of the square of the number. 2669 is not a perfect square. The square root of 2669 is expressed in both radical and exponential form. In radical form, it is expressed as √2669, whereas (2669)^(1/2) in exponential form. √2669 ≈ 51.670, 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 2669
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 method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 2669 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 2669 is broken down into its prime factors.
Step 1: Finding the prime factors of 2669 Breaking it down, we find that 2669 is a prime number itself, meaning it cannot be broken down into smaller prime factors.
Therefore, calculating 2669 using prime factorization is impossible.
Square Root of 2669 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 2669, we need to group it as 69 and 26.
Step 2: Now we need to find n whose square is less than or equal to 26. We can say n is ‘5’ because 5 x 5 = 25 is less than 26. Now the quotient is 5, and after subtracting 25 from 26, the remainder is 1.
Step 3: Bring down the next pair, which is 69, making the new dividend 169. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.
Step 4: Now find n such that 10n x n ≤ 169. We try n = 1, giving us 101 x 1 = 101.
Step 5: Subtract 101 from 169, the difference is 68, and the quotient is 51.
Step 6: 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 6800.
Step 7: Now find the new divisor. We try n = 6 as 1036 x 6 = 6216.
Step 8: Subtracting 6216 from 6800, we get 584.
Step 9: Now the quotient is 51.6.
Step 10: Continue doing these steps until we get a sufficient number of decimal places.
So the square root of √2669 is approximately 51.67.
Square Root of 2669 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 2669 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √2669. The smallest perfect square less than 2669 is 2601 (51^2), and the largest perfect square more than 2669 is 2704 (52^2). √2669 falls between 51 and 52.
Step 2: Now we need to apply the formula that is (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Going by the formula (2669 - 2601) / (2704 - 2601) = 68 / 103 = 0.660. 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 51 + 0.660 = 51.660.
So the square root of 2669 is approximately 51.66.
Common Mistakes and How to Avoid Them in the Square Root of 2669
Students often 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
Forgetting about the negative square root
It is important to make students aware that a number has 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 = 7.07, but there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root 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: √(12+24) = √12 + √24 is the wrong method of using roots. The right way of using roots is √(12+24) = √36.
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 is wrong, the correct answer is √50 ≈ 7.071067.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid 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, resulting in a wrong answer. This may happen either in subtraction or elsewhere.
Square Root of 2669 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √2669?
The area of the square is approximately 7123.89 square units.
Explanation
The area of the square = side^2.
The side length is given as √2669.
Area of the square = side^2
= √2669 x √2669
= 51.67 × 51.67
≈ 2669.
Therefore, the area of the square box is approximately 2669 square units.
Problem 2
A square-shaped building measuring 2669 square feet is built; if each of the sides is √2669, what will be the square feet of half of the building?
1334.5 square feet
Explanation
We can just divide the given area by 2, as the building is square-shaped.
Dividing 2669 by 2, we get 1334.5.
So, half of the building measures 1334.5 square feet.
Problem 3
Calculate √2669 x 5.
Approximately 258.35
Explanation
The first step is to find the square root of 2669, which is approximately 51.67.
The second step is to multiply 51.67 with 5.
So 51.67 x 5 ≈ 258.35.
Problem 4
What will be the square root of (138 + 2531)?
The square root is approximately 51.66.
Explanation
To find the square root, we need to find the sum of (138 + 2531).
138 + 2531 = 2669, and then √2669 ≈ 51.66.
Therefore, the square root of (138 + 2531) is approximately ±51.66.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √2669 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 179.34 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2669 + 38)
= 2 × (51.67 + 38)
= 2 × 89.67
≈ 179.34 units.
FAQ on Square Root of 2669
1.What is √2669 in its simplest form?
2.Mention the factors of 2669.
3.Calculate the square of 2669.
4.Is 2669 a prime number?
5.2669 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 2669?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 2669?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 2669
- Square root: A square root is the inverse of a square. Example: 4^2 = 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.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- 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.
- Approximation: The method of finding a value that is close enough to the right answer, usually with some thought or calculation involved.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
