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, and more. Here, we will discuss the square root of 3050.
The square root is the inverse of the square of the number. 3050 is not a perfect square. The square root of 3050 is expressed in both radical and exponential form. In the radical form, it is expressed as √3050, whereas (3050)^(1/2) in the exponential form. √3050 ≈ 55.224, 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 3050 is broken down into its prime factors.
Step 1: Finding the prime factors of 3050 Breaking it down, we get 2 x 5 x 5 x 61: \(2^1 \times 5^2 \times 61^1\)
Step 2: Now we found out the prime factors of 3050. The second step is to make pairs of those prime factors. Since 3050 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating √3050 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 3050, we need to group it as 50 and 30.
Step 2: Now we need to find n whose square is 30. We can say n as ‘5’ because \(5 \times 5 = 25\), which is lesser than 30. Now the quotient is 5, after subtracting \(30-25\) the remainder is 5.
Step 3: Now let us bring down 50 which is the new dividend. Add the old divisor with the same number 5 + 5 we get 10, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 10n as the new divisor, we need to find the value of n.
Step 5: The next step is finding \(10n \times n \leq 550\). Let's consider n as 5, now \(10 \times 5 \times 5 = 250\).
Step 6: Subtract 550 from 250, the difference is 300, and the quotient is 55.
Step 7: Since the dividend is greater 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 30000.
Step 8: Now we need to find the new divisor that is 110 because \(110 \times 2 = 220\).
Step 9: Subtracting 220 from 30000, we get the result 29800.
Step 10: Now the quotient is 55.2.
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 √3050 is 55.22.
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 3050 using the approximation method.
Step 1: Now we have to find the closest perfect square of √3050. The smallest perfect square less than 3050 is 3025, and the largest perfect square greater than 3050 is 3136. √3050 falls somewhere between 55 and 56.
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 \( (3050 - 3025) \div (3136 - 3025) = 0.25 \). 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 55 + 0.25 = 55.25, so the square root of 3050 is approximately 55.25.
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 √3050?
The area of the square is 3050 square units.
The area of the square = side².
The side length is given as √3050.
Area of the square = side² = √3050 × √3050 = 3050.
Therefore, the area of the square box is 3050 square units.
A square-shaped building measuring 3050 square feet is built; if each of the sides is √3050, what will be the square feet of half of the building?
1525 square feet.
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3050 by 2 = we get 1525.
So half of the building measures 1525 square feet.
Calculate √3050 × 5.
276.12
The first step is to find the square root of 3050, which is approximately 55.22. The second step is to multiply 55.22 with 5. So 55.22 × 5 = 276.12.
What will be the square root of (3025 + 25)?
The square root is 56.
To find the square root, we need to find the sum of (3025 + 25). 3025 + 25 = 3050, and then √3050 ≈ 55.224. Therefore, the square root of (3025 + 25) is approximately 55.224.
Find the perimeter of the rectangle if its length ‘l’ is √3050 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle as 190.44 units.
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√3050 + 40) = 2 × (55.22 + 40) = 2 × 95.22 = 190.44 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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