121 LearnersLast updated on May 26th, 2025
Square Root of 352
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 352.
What is the Square Root of 352?
The square root is the inverse of the square of the number. 352 is not a perfect square. The square root of 352 is expressed in both radical and exponential form. In the radical form, it is expressed as √352, whereas in exponential form it is expressed as (352)^(1/2). √352 ≈ 18.761, 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 352
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 352 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 352 is broken down into its prime factors.
Step 1: Finding the prime factors of 352 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 11: 2^5 x 11
Step 2: Now we have found the prime factors of 352. The second step is to make pairs of those prime factors. Since 352 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating the square root of 352 using prime factorization is not straightforward.
Square Root of 352 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 352, we group it as 52 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 less than or equal to 3. Now the quotient is 1, and after subtracting 1, the remainder is 2.
Step 3: Now let us bring down 52 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 2n. We need to find the value of n such that 2n x n ≤ 252. Let’s consider n as 8, now 28 x 8 = 224.
Step 5: Subtract 224 from 252, the difference is 28, and the quotient is 18.
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 2800.
Step 7: Now we need to find the new divisor that is 186 because 186 x 6 = 1116
Step 8: Subtracting 1116 from 2800, we get the result 1684.
Step 9: Now the quotient is 18.7
Step 10: 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 √352 is approximately 18.76
Square Root of 352 by Approximation Method
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 352 using the approximation method.
Step 1: Now we have to find the closest perfect square of √352.
The smallest perfect square less than 352 is 324, and the largest perfect square greater than 352 is 361. √352 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). Using the formula (352 - 324) / (361 - 324) = 0.756.
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 + 0.756 = 18.756, so the square root of 352 is approximately 18.76.
Common Mistakes and How to Avoid Them in the Square Root of 352
Students do make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes 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 considering 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 square root symbols in proper places
Not using the square root symbol 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 an incorrect 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 roots and square roots 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 352 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √352?
The area of the square is approximately 124.56 square units.
Explanation
The area of the square = side^2.
The side length is given as √352.
Area of the square = side^2 = √352 x √352 = 18.76 × 18.76 ≈ 352
Therefore, the area of the square box is approximately 352 square units.
Problem 2
A square-shaped building measuring 352 square feet is built; if each of the sides is √352, what will be the square feet of half of the building?
176 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 352 by 2 = 176 So half of the building measures 176 square feet.
Problem 3
Calculate √352 x 5.
93.8
Explanation
The first step is to find the square root of 352 which is approximately 18.76, the second step is to multiply 18.76 with 5. So 18.76 x 5 ≈ 93.8
Problem 4
What will be the square root of (352 + 100)?
The square root is 20.
Explanation
To find the square root, we need to find the sum of (352 + 100). 352 + 100 = 452, and then √452 ≈ 21.26.
Therefore, the square root of (352 + 100) is approximately ±21.26.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √352 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 113.52 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√352 + 38) = 2 × (18.76 + 38) = 2 × 56.76 ≈ 113.52 units.
FAQ on Square Root of 352
1.What is √352 in its simplest form?
2.Mention the factors of 352.
3.Calculate the square of 352.
4.Is 352 a prime number?
5.352 is divisible by?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 352?
8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 352?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for the Square Root of 352
- Square root: A square root is the inverse of a square. Example: 4^2 = 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 352 is 2^5 x 11.
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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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