125 LearnersLast updated on May 26th, 2025
Square Root of 318
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 like vehicle design, finance, etc. Here, we will discuss the square root of 318.
What is the Square Root of 318?
The square root is the inverse of the square of the number. 318 is not a perfect square. The square root of 318 is expressed in both radical and exponential form. In the radical form, it is expressed as √318, whereas (318)^(1/2) in the exponential form. √318 ≈ 17.8326, 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 318
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 318 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 318 is broken down into its prime factors.
Step 1: Finding the prime factors of 318 Breaking it down, we get 2 x 3 x 53: 2¹ x 3¹ x 53¹
Step 2: Now we found out the prime factors of 318. The second step is to make pairs of those prime factors. Since 318 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.
Therefore, calculating √318 using prime factorization directly is not feasible.
Square Root of 318 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 318, we need to group it as 18 and 3.
Step 2: Now we need to find n whose square is ≤ 3. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 3. Now the quotient is 1 after subtracting 3 - 1 the remainder is 2.
Step 3: Now let us bring down 18 which is the new dividend. Add the old divisor with the same number 1 + 1 we 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, we need to find the value of n.
Step 5: The next step is finding 2n × n ≤ 218. Let us consider n as 8, now 28 x 8 = 224; we need a value less than 218, so n is 7.
Step 6: Subtract 218 from 217 the difference is 1, and the quotient is 17.
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 100.
Step 8: Now we need to find the new divisor that is 347 because 347 x 2 = 694.
Step 9: Subtracting 694 from 1000 we get the result 306.
Step 10: Now the quotient is 17.83.
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 √318 is approximately 17.83.
Square Root of 318 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 318 using the approximation method.
Step 1: Now we have to find the closest perfect square of √318.
The smallest perfect square less than 318 is 289 (17²) and the largest perfect square greater than 318 is 324 (18²). √318 falls somewhere between 17 and 18.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (318 - 289) ÷ (324 - 289) = 29 ÷ 35 ≈ 0.8286.
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 17 + 0.8286 ≈ 17.83, so the square root of 318 is approximately 17.83.
Common Mistakes and How to Avoid Them in the Square Root of 318
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. 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 usually take the positive square root, as it is the required one.
For example, √50 = 7.07, but there is also -7.07 which should not be forgotten.
Mistake 2
Not adding the 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 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 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between the 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 318 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √318?
The area of the square is approximately 1000.89 square units.
Explanation
The area of the square = side².
The side length is given as √318.
Area of the square = (side)² = (√318) × (√318) ≈ 17.83 × 17.83 ≈ 1000.89.
Therefore, the area of the square box is approximately 1000.89 square units.
Problem 2
A square-shaped building measures 318 square feet; if each of the sides is √318, what will be the square feet of half of the building?
159 square feet.
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 318 by 2 gives us 159.
So half of the building measures 159 square feet.
Problem 3
Calculate √318 × 5.
Approximately 89.15.
Explanation
The first step is to find the square root of 318, which is approximately 17.83.
The second step is to multiply 17.83 by 5.
So, 17.83 × 5 ≈ 89.15.
Problem 4
What will be the square root of (318 + 6)?
The square root is approximately 17.99.
Explanation
To find the square root, we need to find the sum of (318 + 6). 318 + 6 = 324, and then √324 = 18.
Therefore, the square root of (318 + 6) is ±18.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √318 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 111.66 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√318 + 38) = 2 × (17.83 + 38) ≈ 2 × 55.83 ≈ 111.66 units.
FAQ on Square Root of 318
1.What is √318 in its simplest form?
2.Mention the factors of 318.
3.Calculate the square of 318.
4.Is 318 a prime number?
5.318 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 318?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 318?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 318
- 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 a number that is the square of an integer. For example, 16 is a perfect square because it is 4².
- Approximation method: This is a method used to estimate the square root of non-perfect squares by comparing them to nearby perfect squares.
- Long division method: A method used to calculate more accurate values of square roots for non-perfect squares through a systematic division process.
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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.
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