133 LearnersLast updated on May 26th, 2025
Square Root of 253
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 253.
What is the Square Root of 253?
The square root is the inverse of the square of the number. 253 is not a perfect square. The square root of 253 is expressed in both radical and exponential form. In the radical form, it is expressed as √253, whereas (253)^(1/2) in the exponential form. √253 ≈ 15.90597, 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.
Finding the Square Root of 253
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 253 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 253 is broken down into its prime factors:
Step 1: Finding the prime factors of 253 Breaking it down, we get 11 x 23.
Step 2: Since 253 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating 253 using prime factorization is not straightforward.
Square Root of 253 by Long Division Method
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 253, we need to group it as 53 and 2.
Step 2: Now we need to find n whose square is less than or equal to 2. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 2. Now the quotient is 1; after subtracting 1 from 2, the remainder is 1.
Step 3: Now let us bring down 53, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 153. Let us consider n as 7, now 27 x 7 = 189, which is too large, so n is 5.
Step 6: Subtract 125 (25 x 5) from 153; the difference is 28, and the quotient is 15.
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 2800.
Step 8: Now we need to find the new divisor that is 310 because 310 x 9 = 2790. Step 9: Subtracting 2790 from 2800, we get the result 10.
Step 10: Now the quotient is 15.9
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 √253 is approximately 15.90.
Square Root of 253 by Approximation Method
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 253 using the approximation method.
Step 1: Now we have to find the closest perfect square of √253. The smallest perfect square less than 253 is 225, and the largest perfect square greater than 253 is 256. √253 falls somewhere between 15 and 16.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (253 - 225) ÷ (256 - 225) = 28 ÷ 31 ≈ 0.903. 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 15 + 0.903 ≈ 15.903.
So, the square root of 253 is approximately 15.90.
Common Mistakes and How to Avoid Them in the Square Root of 253
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping steps in long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number does have both positive and negative square roots. However, we will only consider the positive square root, as it is the required one.
For example: √253 ≈ 15.90597, there is also -15.90597 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(12 + 24) = √12 + √24 is a wrong method of using roots. The right way of using roots is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √253 ≈ 15.90597, not 15.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly as this will help them avoid mistakes.
For example: √253 and ∛253 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square root of 253 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √253?
The area of the square is approximately 253 square units.
Explanation
The area of the square = side².
The side length is given as √253.
Area of the square = side² = √253 × √253 = 253.
Therefore, the area of the square box is approximately 253 square units.
Problem 2
A square-shaped plot measuring 253 square meters is built; if each of the sides is √253, what will be the square meters of half of the plot?
126.5 square meters
Explanation
We can just divide the given area by 2 as the plot is square-shaped.
Dividing 253 by 2 gives us 126.5.
So half of the plot measures 126.5 square meters.
Problem 3
Calculate √253 × 5.
Approximately 79.53
Explanation
The first step is to find the square root of 253, which is approximately 15.90597.
The second step is to multiply 15.90597 by 5.
So 15.90597 × 5 ≈ 79.53.
Problem 4
What will be the square root of (225 + 28)?
The square root is approximately 15.90.
Explanation
To find the square root, we need to find the sum of (225 + 28).
225 + 28 = 253, and then √253 ≈ 15.90597.
Therefore, the square root of (225 + 28) is approximately ±15.90.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √253 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 107.81 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√253 + 38)
≈ 2 × (15.90597 + 38)
≈ 2 × 53.90597
≈ 107.81 units.
FAQ on Square Root of 253
1.What is √253 in its simplest form?
2.Mention the factors of 253.
3.Calculate the square of 253.
4.Is 253 a prime number?
5.253 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 253?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 253?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 253
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4².
- Approximation: It refers to finding a value that is close enough to the right answer, usually within a certain tolerance. In the context of square roots, it means finding a decimal value close to the actual square root.
- Long division method: A technique used to find the square root of non-perfect squares by dividing the number into pairs of digits, starting from the decimal point, and using a step-by-step division process.
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Jaskaran Singh Saluja
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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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