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 3920.
The square root is the inverse of the square of the number. 3920 is not a perfect square. The square root of 3920 is expressed in both radical and exponential form. In the radical form, it is expressed as √3920, whereas (3920)^(1/2) in the exponential form. √3920 ≈ 62.595, 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 3920 is broken down into its prime factors.
Step 1: Finding the prime factors of 3920 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 7 x 7: 2^4 x 5^1 x 7^2
Step 2: Now we found out the prime factors of 3920. The second step is to make pairs of those prime factors. Since 3920 is not a perfect square, the digits of the number can’t be grouped in pairs completely.
Therefore, calculating 3920 using prime factorization involves taking out the pairs, leading to 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, we need to group the numbers from right to left. In the case of 3920, we need to group it as 92 and 39.
Step 2: Now we need to find 'n' whose square is closest to 39. We can say n as '6' because 6 x 6 = 36, which is lesser than 39. Now the quotient is 6, and after subtracting 36 from 39, the remainder is 3.
Step 3: Now let us bring down 20, which is the new dividend. Add the old divisor with the same number 6 + 6, we get 12, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 12n × n ≤ 320. Let us consider n as 2; now 12 x 2 x 2 = 48.
Step 6: Subtract 320 from 48; the difference is 272, and the quotient is 62.
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 27200.
Step 8: Now we need to find the new divisor. Let us consider n as 2, so we have 124 x 2 = 248.
Step 9: Subtracting 248 from 272, we get the result 24.
Step 10: Now the quotient is 62.5.
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 √3920 ≈ 62.59.
The approximation method is another method for finding the 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 3920 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3920. The smallest perfect square less than 3920 is 3844, and the largest perfect square more than 3920 is 4096. √3920 falls somewhere between 62 and 64.
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 (3920 - 3844) ÷ (4096 - 3844) ≈ 0.5. 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 62 + 0.5 = 62.5, so the square root of 3920 is approximately 62.5.
Students do make mistakes while finding the square root, likewise 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.
Can you help Max find the area of a square box if its side length is given as √3920?
The area of the square is approximately 3920 square units.
The area of the square = side^2.
The side length is given as √3920.
Area of the square = side^2 = √3920 x √3920 = 3920.
Therefore, the area of the square box is approximately 3920 square units.
A square-shaped building measuring 3920 square feet is built; if each of the sides is √3920, what will be the square feet of half of the building?
1960 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3920 by 2, we get 1960.
So half of the building measures 1960 square feet.
Calculate √3920 x 5.
Approximately 312.975
The first step is to find the square root of 3920, which is approximately 62.595.
The second step is to multiply 62.595 with 5.
So 62.595 x 5 ≈ 312.975.
What will be the square root of (3900 + 20)?
The square root is approximately 62.595.
To find the square root, we need to find the sum of (3900 + 20).
3900 + 20 = 3920, and then √3920 ≈ 62.595.
Therefore, the square root of (3900 + 20) is approximately ±62.595.
Find the perimeter of the rectangle if its length ‘l’ is √3920 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 201.19 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3920 + 38)
= 2 × (62.595 + 38)
= 2 × 100.595
= 201.19 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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