101 LearnersLast updated on May 26th, 2025
Square Root of 1322
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 such as vehicle design, finance, etc. Here, we will discuss the square root of 1322.
What is the Square Root of 1322?
The square root is the inverse of the square of the number. 1322 is not a perfect square. The square root of 1322 is expressed in both radical and exponential form. In the radical form, it is expressed as √1322, whereas (1322)^(1/2) in exponential form. √1322 ≈ 36.3601, 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 1322
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, 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 1322 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1322 is broken down into its prime factors.
Step 1: Finding the prime factors of 1322 Breaking it down, we get 2 x 661. Upon further factorization of 661, we get 661 = 19 x 37. Therefore, 1322 = 2 x 19 x 37.
Step 2: After finding the prime factors of 1322, we notice that they cannot be grouped into pairs since 1322 is not a perfect square. Therefore, calculating √1322 using prime factorization is not feasible.
Square Root of 1322 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 1322, we need to group it as 22 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, and after subtracting, 13 - 9, the remainder is 4.
Step 3: Bring down the next pair of numbers, which is 22, making the new dividend 422. Add the old divisor, 3, with itself, giving us 6, which will be part of our new divisor, 6n.
Step 4: We need to find n such that 6n x n ≤ 422. Let us consider n as 6, then 66 x 6 = 396, which is less than 422.
Step 5: Subtract 396 from 422, giving a remainder of 26, and the quotient is 36.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point and bring down two zeros. The new dividend is 2600.
Step 7: Find a new digit for the divisor to be used with the new dividend. This digit is 4 because 724 x 4 = 2896, which exceeds 2600. We try 3, giving us 723 x 3 = 2169.
Step 8: Subtract 2169 from 2600, yielding 431. The quotient now is 36.3.
Step 9: Continue these steps by bringing down more pairs of zeros, refining the remainder, and extending the quotient.
Square Root of 1322 by Approximation Method
The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Let us learn how to find the square root of 1322 using the approximation method.
Step 1: We need to find the closest perfect squares around 1322. The smallest perfect square less than 1322 is 1225 (35^2), and the largest perfect square greater than 1322 is 1369 (37^2). √1322 falls somewhere between 35 and 37.
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 (1322 - 1225) / (1369 - 1225) = 0.674. 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 35 + 0.674 = 35.674. Thus, the square root of 1322 is approximately 35.674.
Common Mistakes and How to Avoid Them in the Square Root of 1322
Students often make mistakes while finding square roots, 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 typically consider only 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.
Square Root of 1322 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1322?
The area of the square is approximately 1322 square units.
Explanation
The area of the square = side².
The side length is given as √1322.
Area of the square = side² = √1322 x √1322 = 1322.
Therefore, the area of the square box is approximately 1322 square units.
Problem 2
A square-shaped building measuring 1322 square feet is built; if each of the sides is √1322, what will be the square feet of half of the building?
661 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1322 by 2 = we get 661.
So half of the building measures 661 square feet.
Problem 3
Calculate √1322 x 5.
Approximately 181.8
Explanation
The first step is to find the square root of 1322, which is approximately 36.3601.
The second step is to multiply 36.3601 with 5.
So 36.3601 x 5 ≈ 181.8.
Problem 4
What will be the square root of (1300 + 22)?
The square root is approximately 36.3601.
Explanation
To find the square root, we need to find the sum of (1300 + 22). 1300 + 22 = 1322, and then √1322 ≈ 36.3601.
Therefore, the square root of (1300 + 22) is approximately ±36.3601.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1322 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 148.72 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1322 + 38) ≈ 2 × (36.3601 + 38) = 2 × 74.3601 ≈ 148.72 units.
FAQ on Square Root of 1322
1.What is √1322 in its simplest form?
2.Mention the factors of 1322.
3.Calculate the square of 1322.
4.Is 1322 a prime number?
5.1322 is divisible by?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 1322?
8.How do technology and digital tools in Oman support learning Algebra and Square Root of 1322?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for the Square Root of 1322
- 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 ≠ 0 and p and q are integers.
- Long division method: A method to find the square root of non-perfect squares by dividing and finding digits sequentially.
- Approximation method: A method used to find the square root by identifying nearby perfect squares and estimating the value between them.
- Perfect square: A perfect square is a number that is the square of an integer. Example: 144 is a perfect square since it is 12².
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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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