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 various fields including vehicle design, finance, etc. Here, we will discuss the square root of 3626.
The square root is the inverse of the square of the number. 3626 is not a perfect square. The square root of 3626 is expressed in both radical and exponential form. In the radical form, it is expressed as √3626, whereas (3626)^(1/2) in the exponential form. √3626 ≈ 60.209, 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 the 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 3626 is broken down into its prime factors:
Step 1: Finding the prime factors of 3626 Breaking it down, we get 2 x 1813, where 1813 is a prime number. Since 3626 is not a perfect square, calculating √3626 using prime factorization is not straightforward as the digits cannot be grouped into pairs.
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 3626, we need to group it as 26 and 36.
Step 2: Now we need to find n whose square is less than or equal to 36. We can say n is 6 because 6^2 = 36. Now the quotient is 6 after subtracting 36 from 36, the remainder is 0.
Step 3: Bring down 26, which is the new dividend. Add the old divisor with the same number, 6 + 6, we get 12 as the new divisor.
Step 4: We need to find a number n such that 12n × n ≤ 2600. Let's try n = 2, then 122 × 2 = 244
Step 5: Subtract 244 from 260, and the difference is 16.
Step 6: Since the dividend is less than the divisor, we add a decimal point and bring down two zeroes, making the new dividend 1600.
Step 7: Now find the new divisor, 120, and repeat the steps until you achieve the desired precision.
So the square root of √3626 is approximately 60.209.
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 3626 using the approximation method.
Step 1: Find the closest perfect squares around 3626. The closest perfect square below 3626 is 3600 and above is 3721. √3626 falls between 60 and 61.
Step 2: Using the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (3626 - 3600) / (3721 - 3600) ≈ 0.217 Add this decimal to 60: 60 + 0.217 ≈ 60.217
So the square root of 3626 is approximately 60.209 when calculated more precisely.
Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let us look at a few of these mistakes in detail.
Can you help Max find the area of a square box if its side length is given as √3626?
The area of the square is 3626 square units.
The area of the square = side².
The side length is given as √3626.
Area of the square = side² = √3626 × √3626 = 3626.
Therefore, the area of the square box is 3626 square units.
A square-shaped building measuring 3626 square feet is built; if each of the sides is √3626, what will be the square feet of half of the building?
1813 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3626 by 2 gives 1813.
So half of the building measures 1813 square feet.
Calculate √3626 × 5.
301.045
The first step is to find the square root of 3626, which is approximately 60.209.
The second step is to multiply 60.209 with 5.
So 60.209 × 5 = 301.045.
What will be the square root of (3600 + 26)?
The square root is 60.209.
To find the square root, we need to find the sum of (3600 + 26).
3600 + 26 = 3626, and then √3626 ≈ 60.209.
Therefore, the square root of (3600 + 26) is approximately ±60.209.
Find the perimeter of the rectangle if its length ‘l’ is √3626 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 196.418 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3626 + 38)
= 2 × (60.209 + 38)
= 2 × 98.209
= 196.418 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.
: He loves to play the quiz with kids through algebra to make kids love it.