117 LearnersLast updated on May 26th, 2025
Square Root of 351
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 351.
What is the Square Root of 351?
The square root is the inverse of the square of the number. 351 is not a perfect square. The square root of 351 is expressed in both radical and exponential forms. In the radical form, it is expressed as √351, whereas (351)^(1/2) in the exponential form. √351 ≈ 18.73499, 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 351
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 351 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 351 is broken down into its prime factors:
Step 1: Finding the prime factors of 351 Breaking it down, we get 3 x 3 x 3 x 13: 3^3 x 13^1
Step 2: Now we found out the prime factors of 351. The second step is to make pairs of those prime factors. Since 351 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating √351 using prime factorization is not feasible.
Square Root of 351 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 351, we need to group it as 51 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 1 x 1, the remainder is 2.
Step 3: Now let us bring down 51 which is the new dividend. Add the old divisor with the same number: 1 + 1 = 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 x n ≤ 251. Let us consider n as 8, now 28 x 8 = 224.
Step 6: Subtract 224 from 251, the difference is 27, and the quotient is 18.
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 2700.
Step 8: Now we need to find the new divisor that is 187 because 1878 x 8 = 1504.
Step 9: Subtracting 1504 from 2700, we get the result 1196.
Step 10: Now the quotient is 18.7
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 √351 is approximately 18.73
Square Root of 351 by Approximation Method
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 351 using the approximation method.
Step 1: Now we have to find the closest perfect square of √351
The smallest perfect square less than 351 is 324, and the largest perfect square greater than 351 is 361. √351 falls somewhere between 18 and 19.
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 (351 - 324) / (361 - 324) = 0.73
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 18 + 0.73 = 18.73, so the square root of 351 is approximately 18.73.
Common Mistakes and How to Avoid Them in the Square Root of 351
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.
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 = 7.071, there is also -7.071, 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. 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, 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 keep away from 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. This may either happen in subtracting or elsewhere.
Square root of 351 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √351?
The area of the square is 351 square units.
Explanation
The area of the square = side².
The side length is given as √351.
Area of the square = side² = √351 x √351 = 351.
Therefore, the area of the square box is 351 square units.
Problem 2
A square-shaped building measuring 351 square feet is built; if each of the sides is √351, what will be the square feet of half of the building?
175.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 351 by 2 = we get 175.5
So half of the building measures 175.5 square feet.
Problem 3
Calculate √351 x 5.
93.67
Explanation
The first step is to find the square root of 351 which is approximately 18.73, the second step is to multiply 18.73 with 5. So 18.73 x 5 = 93.65
Problem 4
What will be the square root of (324 + 27)?
The square root is approximately 19.
Explanation
To find the square root, we need to find the sum of (324 + 27). 324 + 27 = 351, and then √351 ≈ 18.73.
Therefore, the square root of (324 + 27) is approximately ±18.73.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √351 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle as 117.47 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√351 + 40) = 2 × (18.73 + 40) = 2 × 58.73 = 117.47 units.
FAQ on Square Root of 351
1.What is √351 in its simplest form?
2.Mention the factors of 351.
3.Calculate the square of 351.
4.Is 351 a prime number?
5.351 is divisible by?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square Root of 351?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 351?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 351
- Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse operation is the square root, which is √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a ratio of two integers, where the denominator is not zero.
- Perfect square: A perfect square is an integer that is the square of an integer. For example: 1, 4, 9, 16, and 25 are perfect squares.
- Long division method: A method used to find the square root of non-perfect squares through a series of calculated steps.
- Decimal approximation: An estimated value of an irrational number expressed in decimal form, often rounded to a certain number of decimal places.
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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.
Fun Fact
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