Last updated on May 26th, 2025
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.
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.
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:
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.
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.
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.
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.
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.
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.
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
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.
Calculate √2669 x 5.
Approximately 258.35
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.
What will be the square root of (138 + 2531)?
The square root is approximately 51.66.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√2669 + 38)
= 2 × (51.67 + 38)
= 2 × 89.67
≈ 179.34 units.
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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