121 LearnersLast updated on May 26th, 2025
Square Root of 1352
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 1352.
What is the Square Root of 1352?
The square root is the inverse of the square of the number. 1352 is not a perfect square. The square root of 1352 is expressed in both radical and exponential form. In the radical form, it is expressed as √1352, whereas 1352^(1/2) in the exponential form. √1352 ≈ 36.758, 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 1352
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 1352 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1352 is broken down into its prime factors.
Step 1: Finding the prime factors of 1352
Breaking it down, we get 2 x 2 x 2 x 13 x 13: 2^3 x 13^2
Step 2: Now we found out the prime factors of 1352. Since 1352 is not a perfect square, the digits of the number can’t be grouped in pairs completely. Therefore, calculating the square root of 1352 using prime factorization gives us √(2^3 x 13^2) = 2 x 13√2 = 26√2, which is approximately 36.758.
Square Root of 1352 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 1352, we need to group it as 52 and 13.
Step 2: Now we need to find n whose square is less than or equal to 13. We can say n as '3' because 3 x 3 = 9, which is less than 13. Now the quotient is 3. After subtracting 9 from 13, the remainder is 4.
Step 3: Now let us bring down 52, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor; we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 452. Let us consider n as 7, now 67 x 7 = 469, which is too large, so we try n as 6.
Step 6: Now, 66 x 6 = 396. Subtracting 452 from 396, the difference is 56, and the quotient is 36.
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 5600.
Step 8: Now we need to find the new divisor that is 732 because 732 x 7 = 5124.
Step 9: Subtracting 5124 from 5600, we get the result 476.
Step 10: Now the quotient is 36.7
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose there is no decimal value; continue till the remainder is zero.
So the square root of √1352 is approximately 36.76.
Square Root of 1352 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 1352 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1352. The smallest perfect square less than 1352 is 1296 (36^2), and the largest perfect square greater than 1352 is 1369 (37^2). √1352 falls somewhere between 36 and 37.
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 (1352 - 1296) ÷ (1369 - 1296) = 56 ÷ 73 ≈ 0.767 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 36 + 0.767 ≈ 36.767. So the square root of 1352 is approximately 36.767.
Common Mistakes and How to Avoid Them in the Square Root of 1352
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 ≈ 7.07; there is also -7.07 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 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 ≈ 7.071067.
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 of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1352 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1352?
The area of the square is 1352 square units.
Explanation
The area of the square = side^2.
The side length is given as √1352.
Area of the square = side^2 = √1352 x √1352 = 1352.
Therefore, the area of the square box is 1352 square units.
Problem 2
A square-shaped building measuring 1352 square feet is built; if each of the sides is √1352, what will be the square feet of half of the building?
676 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1352 by 2 = we get 676.
So half of the building measures 676 square feet.
Problem 3
Calculate √1352 x 5.
183.79
Explanation
The first step is to find the square root of 1352, which is approximately 36.76.
The second step is to multiply 36.76 with 5.
So 36.76 x 5 = 183.79.
Problem 4
What will be the square root of (1300 + 52)?
The square root is approximately 36.76
Explanation
To find the square root, we need to find the sum of (1300 + 52). 1300 + 52 = 1352, and then √1352 ≈ 36.76.
Therefore, the square root of (1300 + 52) is approximately ±36.76.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1352 units and the width ‘w’ is 40 units.
We find the perimeter of the rectangle as 153.52 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1352 + 40) = 2 × (36.76 + 40) = 2 × 76.76 = 153.52 units.
FAQ on Square Root of 1352
1.What is √1352 in its simplest form?
2.Mention the factors of 1352.
3.Calculate the square of 1352.
4.Is 1352 a prime number?
5.1352 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 1352?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 1352?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 1352
- 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 a positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Divisor: A divisor is a number by which another number is to be divided.
- Approximation: The process of finding a value or quantity that is close to but not the exact number.
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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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