124 LearnersLast updated on May 26th, 2025
Square Root of 1312
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 fields such as vehicle design and finance. Here, we will discuss the square root of 1312.
What is the Square Root of 1312?
The square root is the inverse of the square of a number. 1312 is not a perfect square. The square root of 1312 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1312, whereas in exponential form, it is (1312)^(1/2). √1312 ≈ 36.225, 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 1312
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 1312 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1312 is broken down into its prime factors:
Step 1: Finding the prime factors of 1312
Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 41: 2^5 x 41
Step 2: Now we found out the prime factors of 1312. The second step is to make pairs of those prime factors. Since 1312 is not a perfect square, calculating √1312 using prime factorization is challenging without further steps.
Square Root of 1312 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we 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, group the numbers from right to left. In the case of 1312, group it as 12 and 13.
Step 2: Find a number n whose square is less than or equal to 13. Here, n is 3 because 3 x 3 = 9.
Step 3: Subtract 9 from 13; the remainder is 4. Bring down the next pair of digits (12), making the new dividend 412.
Step 4: Double the previous divisor (3), giving us 6. Find a digit x such that 6x multiplied by x is less than or equal to 412. The value of x is 6 because 66 x 6 = 396.
Step 5: Subtract 396 from 412; the remainder is 16. Continue the process with decimal points to get a more precise value of the square root.
Step 6: Continue until you have the desired decimal precision. The square root of 1312 is approximately 36.225.
Square Root of 1312 by Approximation Method
The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 1312 using the approximation method.
Step 1: Find the closest perfect square to √1312. The nearest perfect squares are 1296 (36^2) and 1369 (37^2). √1312 falls between 36 and 37.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (1312 - 1296) / (1369 - 1296) = 16 / 73 ≈ 0.219
Step 3: Add this decimal to 36 to get an approximate square root: 36 + 0.219 ≈ 36.219. So, the square root of 1312 is approximately 36.219.
Common Mistakes and How to Avoid Them in the Square Root of 1312
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in the long division method. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we usually consider only the positive square root, as it is often 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 symbol properly is another mistake. It's important to simplify the numbers inside the square root first.
For example, √(12 + 24) ≠ √12 + √24.
The correct method is √(12 + 24) = √36.
Mistake 3
Not finding the correct value of a non-perfect square
The first step is to simplify the numbers inside the square root to avoid 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 learn the difference between cube root and square root to 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. Many students might skip a step accidentally, leading to a wrong answer. This may happen in subtracting or elsewhere.
Square Root of 1312 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1312?
The area of the square is approximately 1721.225 square units.
Explanation
The area of the square = side^2.
The side length is given as √1312.
Area of the square = side^2 = √1312 x √1312 ≈ 36.225 x 36.225 = 1312.
Therefore, the area of the square box is approximately 1312 square units.
Problem 2
A square-shaped building measuring 1312 square feet is built; if each of the sides is √1312, what will be the square feet of half of the building?
656 square feet
Explanation
We can divide the given area by 2 because the building is square-shaped.
Dividing 1312 by 2 gives us 656.
So half of the building measures 656 square feet.
Problem 3
Calculate √1312 x 5.
Approximately 181.125
Explanation
The first step is to find the square root of 1312, which is approximately 36.225.
The second step is to multiply 36.225 by 5. So, 36.225 x 5 ≈ 181.125.
Problem 4
What will be the square root of (1300 + 12)?
The square root is approximately 36.225
Explanation
To find the square root, compute the sum of 1300 + 12, which equals 1312.
Then, √1312 ≈ 36.225.
Therefore, the square root of (1300 + 12) is approximately ±36.225.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √1312 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 172.45 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1312 + 50) ≈ 2 × (36.225 + 50) = 2 × 86.225 ≈ 172.45 units.
FAQ on Square Root of 1312
1.What is √1312 in its simplest form?
2.Mention the factors of 1312.
3.Calculate the square of 1312.
4.Is 1312 a prime number?
5.1312 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 1312?
8.How do technology and digital tools in India support learning Algebra and Square Root of 1312?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 1312
- Square root: A square root is the inverse of a square. For example, 6^2 = 36, and the inverse is √36 = 6.
- Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Prime factorization: Prime factorization involves breaking down a number into its prime factors.
- Long division method: A technique used to find the square root of non-perfect squares through a step-by-step division process.
- Approximation method: A method to estimate the square root by finding numbers between which the given number's square root lies and using them to calculate an approximate value.
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Jaskaran Singh Saluja
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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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