136 LearnersLast updated on May 26th, 2025
Square Root of 307
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 307.
What is the Square Root of 307?
The square root is the inverse of the square of the number. 307 is not a perfect square. The square root of 307 is expressed in both radical and exponential form. In the radical form, it is expressed as √307, whereas (307)^(1/2) in exponential form. √307 ≈ 17.52142, 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 307
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:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 307 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 307 is broken down into its prime factors.
Step 1: Finding the prime factors of 307 Since 307 is a prime number, it cannot be broken down further into other prime factors.
Step 2: Now we found out the prime factors of 307. As 307 is not a perfect square, calculating 307 using prime factorization is not straightforward.
Square Root of 307 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 307, we need to group it as 07 and 3.
Step 2: Now we need to find n whose square is less than or equal to 3. We can say n as ‘1’ because 1 x 1 is less than or equal to 3. Now the quotient is 1, and after subtracting 1 from 3, the remainder is 2.
Step 3: Now let us bring down 07, making the new dividend 207. Add the old divisor with the same number 1 + 1; we get 2, which will be our new divisor.
Step 4: With the new divisor 2, find 2n such that 2n x n ≤ 207. Let us consider n as 7, then 27 x 7 = 189.
Step 5: Subtract 189 from 207; the difference is 18, and the quotient is 17.
Step 6: 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 1800.
Step 7: Now we need to find the new divisor by considering 345 because 345 x 5 = 1725.
Step 8: Subtracting 1725 from 1800, we get the result 75.
Step 9: Now the quotient is 17.5.
Step 10: 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 √307 ≈ 17.52.
Square Root of 307 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 307 using the approximation method.
Step 1: Now we have to find the closest perfect square of √307. The smallest perfect square less than 307 is 289 (17²), and the largest perfect square greater than 307 is 324 (18²). √307 falls somewhere between 17 and 18.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (307 - 289) / (324 - 289) = 18 / 35 ≈ 0.514. Using this 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 17 + 0.514 ≈ 17.514, so the square root of 307 is approximately 17.514.
Common Mistakes and How to Avoid Them in the Square Root of 307
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping 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 be taking only the positive square root, as it is the required one.
For example, √50 = 7.07, there is also -7.07, which should not be forgotten.
Mistake 2
Not adding the square root symbol in the 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 the 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, √50 = 7 is wrong; the correct answer is √50 ≈ 7.071.
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, √50 and ∛50 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 307 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √307?
The area of the square is approximately 307 square units.
Explanation
The area of the square = side².
The side length is given as √307.
Area of the square = side² = √307 x √307 = 307.
Therefore, the area of the square box is approximately 307 square units.
Problem 2
A square-shaped garden measuring 307 square meters is built; if each of the sides is √307, what will be the square meters of half of the garden?
153.5 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 307 by 2 gives us 153.5.
So half of the garden measures 153.5 square meters.
Problem 3
Calculate √307 x 5.
Approximately 87.6
Explanation
The first step is to find the square root of 307, which is approximately 17.52.
The second step is to multiply 17.52 by 5.
So, 17.52 x 5 ≈ 87.6.
Problem 4
What will be the square root of (307 + 12)?
The square root is approximately 18.
Explanation
To find the square root, we need to find the sum of (307 + 12). 307 + 12 = 319.
√319 ≈ 17.86, which rounds to approximately 18.
Therefore, the square root of (307 + 12) is approximately ±18.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √307 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as approximately 75.04 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√307 + 20) ≈ 2 × (17.52 + 20) ≈ 2 × 37.52 ≈ 75.04 units.
FAQ on Square Root of 307
1.What is √307 in its simplest form?
2.Mention the factors of 307.
3.Calculate the square of 307.
4.Is 307 a prime number?
5.307 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 307?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 307?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 307
- Square root: A square root is the inverse operation of squaring a number. 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.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Long division method: A technique used to divide large numbers and to find square roots of non-perfect squares by breaking down the division process into a series of easier steps.
- Approximation method: A method used to estimate the square root of a number by identifying the closest perfect squares and using a formula to find a more precise value.
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About BrightChamps in Bahrain
Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
