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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 3900.
The square root is the inverse of the square of the number. 3900 is not a perfect square. The square root of 3900 is expressed in both radical and exponential form. In the radical form, it is expressed as √3900, whereas (3900)^(1/2) in exponential form. √3900 ≈ 62.44998, 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 3900 is broken down into its prime factors.
Step 1: Finding the prime factors of 3900 Breaking it down, we get 2 x 2 x 3 x 5 x 5 x 13: 2² x 3¹ x 5² x 13¹
Step 2: Now we found the prime factors of 3900. The second step is to make pairs of those prime factors. Since 3900 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating 3900 using prime factorization will yield an approximate value.
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, group the numbers from right to left. In the case of 3900, we need to group it as 39 and 00.
Step 2: Find a number whose square is less than or equal to 39. We can say n is ‘6’ because 6 x 6 = 36, which is less than 39. Now the quotient is 6 after subtracting 39 - 36, the remainder is 3.
Step 3: Bring down 00 to make the new dividend 300. Add the old divisor with the same number 6 + 6 to get 12, which will be our new divisor.
Step 4: Find a digit n such that 12n x n ≤ 300. Let n be 2. So, 122 x 2 = 244.
Step 5: Subtract the result from the dividend: 300 - 244 = 56.
Step 6: Since the dividend is less than the divisor, add a decimal point. Adding a decimal point allows us to add two zeroes to the dividend. The new dividend is 5600.
Step 7: Find the new divisor that is 124, because 1244 x 4 = 4976.
Step 8: Subtracting 4976 from 5600 gives the result 624.
Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.
So the square root of √3900 is approximately 62.45.
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 3900 using the approximation method.
Step 1: We have to find the closest perfect square to √3900. The smallest perfect square less than 3900 is 3600, and the largest perfect square more than 3900 is 4096. √3900 falls somewhere between 60 and 64.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using this formula: (3900 - 3600) / (4096 - 3600) = 300 / 496 ≈ 0.6048 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 60 + 0.6048 ≈ 60.60, so the square root of 3900 is approximately 62.45.
Students do make mistakes while finding the square root, such as forgetting about the negative square root and skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max calculate the perimeter of a square if its side length is given as √3900?
The perimeter of the square is approximately 249.8 units.
The perimeter of a square = 4 × side length. The side length is given as √3900.
Perimeter = 4 × √3900 ≈ 4 × 62.45 = 249.8 units.
Therefore, the perimeter of the square is approximately 249.8 units.
A square-shaped plot measuring 3900 square feet is built; if each of the sides is √3900, what will be the square feet of half of the plot?
1950 square feet
We can just divide the given area by 2 as the plot is square-shaped.
Dividing 3900 by 2 gives us 1950.
So half of the plot measures 1950 square feet.
Calculate √3900 × 3.
187.35
The first step is to find the square root of 3900, which is approximately 62.45.
The second step is to multiply 62.45 by 3.
So 62.45 × 3 = 187.35.
What will be the square root of (3600 + 300)?
The square root is approximately 62.45.
To find the square root, we need to find the sum of (3600 + 300).
3600 + 300 = 3900, and then √3900 ≈ 62.45.
Therefore, the square root of (3600 + 300) is approximately ±62.45.
Find the perimeter of the rectangle if its length ‘l’ is √3900 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 224.9 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√3900 + 50)
= 2 × (62.45 + 50)
= 2 × 112.45
= 224.9 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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