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 such as engineering, finance, etc. Here, we will discuss the square root of 2900.
The square root is the inverse of the square of the number. 2900 is not a perfect square. The square root of 2900 is expressed in both radical and exponential forms. In the radical form, it is expressed as √2900, whereas (2900)^(1/2) in the exponential form. The square root of 2900 is approximately 53.851648, 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 2900 is broken down into its prime factors:
Step 1: Finding the prime factors of 2900 Breaking it down, we get 2 x 2 x 5 x 5 x 29: 2^2 x 5^2 x 29
Step 2: Now we found out the prime factors of 2900. The second step is to make pairs of those prime factors. Since 2900 is not a perfect square, therefore the digits of the number can’t be grouped into pairs completely. Therefore, calculating the square root of 2900 using prime factorization is not straightforward.
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 2900, we need to group it as 29 and 00.
Step 2: Now we need to find n whose square is less than or equal to 29. We can say n as ‘5’ because 5 × 5 = 25, which is less than 29. Now the quotient is 5, and after subtracting 29 - 25, the remainder is 4.
Step 3: Now let us bring down 00, which is the new dividend. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and the 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 × n ≤ 400. Let us consider n as 3, now 10 × 3 × 3 = 90
Step 6: Subtract 400 from 90, the difference is 310, and the quotient is 53
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 31000.
Step 8: Now we need to find the new divisor that is 107 because 1077 × 7 = 7539
Step 9: Subtracting 7539 from 31000 we get the result 23461.
Step 10: Now the quotient is 53.8
Step 11: 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 √2900 is approximately 53.85
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 2900 using the approximation method.
Step 1: Now we have to find the closest perfect square of √2900. The smallest perfect square less than 2900 is 2809 (which is 53^2), and the largest perfect square is 2916 (which is 54^2). √2900 falls somewhere between 53 and 54.
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 (2900 - 2809) ÷ (2916 - 2809) = 91 ÷ 107 = 0.850467 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 53 + 0.850467 = 53.850467, so the square root of 2900 is approximately 53.85.
Students do make mistakes while finding the square root, like 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 √2900?
The area of the square is 2900 square units.
The area of the square = side^2.
The side length is given as √2900.
Area of the square = side^2 = √2900 x √2900 = 2900 square units.
A square-shaped field measuring 2900 square feet is built; if each of the sides is √2900, what will be the square feet of half of the field?
1450 square feet
We can just divide the given area by 2 as the field is square-shaped.
Dividing 2900 by 2 = we get 1450
So half of the field measures 1450 square feet.
Calculate √2900 x 5.
Approximately 269.25824
The first step is to find the square root of 2900, which is approximately 53.851648.
The second step is to multiply 53.851648 by 5.
So 53.851648 x 5 = approximately 269.25824
What will be the square root of (2500 + 400)?
The square root is 54
To find the square root, we need to find the sum of (2500 + 400)
2500 + 400 = 2900, and then √2900 ≈ 53.85.
Therefore, for simplicity, we can round it to 54.
Find the perimeter of the rectangle if its length ‘l’ is √2900 units and the width ‘w’ is 50 units.
We find the perimeter of the rectangle as approximately 207.703296 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√2900 + 50)
= 2 × (53.851648 + 50)
= 2 × 103.851648
≈ 207.703296 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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