127 LearnersLast updated on May 26th, 2025
Square Root of 1412
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 1412.
What is the Square Root of 1412?
The square root is the inverse of the square of the number. 1412 is not a perfect square. The square root of 1412 is expressed in both radical and exponential form. In the radical form, it is expressed as √1412, whereas (1412)^(1/2) in the exponential form. √1412 ≈ 37.558, 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 1412
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 1412 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now, let us look at how 1412 is broken down into its prime factors:
Step 1: Finding the prime factors of 1412 Breaking it down, we get 2 × 2 × 353: 2^2 × 353
Step 2: Now, we have found the prime factors of 1412. The second step is to make pairs of those prime factors. Since 1412 is not a perfect square, therefore, the digits of the number can’t be grouped in pairs.
Therefore, calculating 1412 using prime factorization is impossible.
Square Root of 1412 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 1412, we need to group it as 12 and 14.
Step 2: Now, we need to find n whose square is less than or equal to 14. We can say n as ‘3’ because 3 × 3 = 9 is lesser than 14. Now the quotient is 3. After subtracting 9 from 14, the remainder is 5.
Step 3: Now, let us bring down 12 which is the new dividend. Add the old divisor with the same number 3 + 3, we get 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, and we need to find the value of n.
Step 5: The next step is finding 6n × n ≤ 512. Let us consider n as 8. Now, 68 × 8 = 544
Step 6: Since 544 is greater than 512, we consider n as 7. Therefore, 67 × 7 = 469
Step 7: Subtract 469 from 512; the difference is 43. The quotient is 37.
Step 8: 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 4300.
Step 9: Now, we need to find the new divisor, which is 754 because 754 × 4 = 3016
Step 10: Subtracting 3016 from 4300, we get the result 1284.
Step 11: The quotient is now 37.4. Step 12: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.
So, the square root of √1412 is approximately 37.558.
Square Root of 1412 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 1412 using the approximation method.
Step 1: Now we have to find the closest perfect square of √1412.
The smallest perfect square closest to 1412 is 1369, and the largest perfect square is 1444. √1412 falls somewhere between 37 and 38.
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 (1412 - 1369) ÷ (1444 - 1369) = 43 ÷ 75 ≈ 0.573
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 37 + 0.573 = 37.573.
So, the square root of 1412 is approximately 37.573.
Common Mistakes and How to Avoid Them in the Square Root of 1412
Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. 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, and 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 ≈ 7.071.
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 of the sum. This may either happen in subtracting or elsewhere.
Square Root of 1412 Examples
Problem 1
Can you help Alex find the area of a square box if its side length is given as √1412?
The area of the square is approximately 1994.064 square units.
Explanation
The area of the square = side^2.
The side length is given as √1412.
Area of the square = side^2 = √1412 × √1412 ≈ 37.558 × 37.558 ≈ 1994.064.
Therefore, the area of the square box is approximately 1994.064 square units.
Problem 2
A square-shaped building measuring 1412 square feet is built; if each of the sides is √1412, what will be the square feet of half of the building?
706 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1412 by 2, we get 706.
So, half of the building measures 706 square feet.
Problem 3
Calculate √1412 × 5.
Approximately 187.79
Explanation
The first step is to find the square root of 1412, which is approximately 37.558.
The second step is to multiply 37.558 with 5.
So, 37.558 × 5 ≈ 187.79.
Problem 4
What will be the square root of (1412 + 88)?
The square root is approximately 39.24
Explanation
To find the square root, we need to find the sum of (1412 + 88). 1412 + 88 = 1500, and then √1500 ≈ 39.24.
Therefore, the square root of (1412 + 88) is approximately ±39.24.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1412 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 151.12 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1412 + 38) = 2 × (37.558 + 38) = 2 × 75.558 ≈ 151.12 units.
FAQ on Square Root of 1412
1.What is √1412 in its simplest form?
2.Mention the factors of 1412.
3.Calculate the square of 1412.
4.Is 1412 a prime number?
5.1412 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 1412?
8.How do technology and digital tools in Singapore support learning Algebra and Square Root of 1412?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for the Square Root of 1412
- Square root: A square root is the inverse of a square. For 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.
- Long division method: A mathematical method used to divide large numbers and find square roots of non-perfect squares through a series of steps.
- Approximation method: A technique for estimating the value of the square root by finding the nearest perfect squares and calculating a decimal approximation.
- Prime factorization: Breaking down a composite number into a product of its prime factors.
Explore More algebra
About BrightChamps in Singapore
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
: He loves to play the quiz with kids through algebra to make kids love it.
