115 LearnersLast updated on May 26th, 2025
Square Root of 1413
If a number is multiplied by the same number, the result is a square. The inverse of a square is a square root. The square root is used in fields like vehicle design, finance, etc. Here, we will discuss the square root of 1413.
What is the Square Root of 1413?
The square root is the inverse of the square of a number. 1413 is not a perfect square. The square root of 1413 is expressed in both radical and exponential form. In the radical form, it is expressed as √1413, whereas (1413)^(1/2) in the exponential form. √1413 ≈ 37.58989, 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 1413
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 1413 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1413 is broken down into its prime factors:
Step 1: Finding the prime factors of 1413. Breaking it down, we get 3 x 3 x 157: 3^2 x 157
Step 2: Now we found out the prime factors of 1413. The second step is to make pairs of those prime factors. Since 1413 is not a perfect square, the digits of the number can’t be grouped in pairs.
Therefore, calculating the square root of 1413 using prime factorization is impossible.
Square Root of 1413 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 1413, we need to group it as 13 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 x 3 = 9 is less than 14. Now the quotient is 3, and after subtracting 9 from 14, the remainder is 5.
Step 3: Now let us bring down 13, 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: We need to find n such that 6n x n ≤ 513. Let us consider n as 8, now 68 x 8 = 544.
Step 5: Since 544 is greater than 513, we try with n as 7, now 67 x 7 = 469.
Step 6: Subtract 469 from 513; the difference is 44, and the quotient is 37.
Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 4400.
Step 8: Now we need to find the new divisor by adding 7 to the previous divisor, making it 74. 74n x n ≤ 4400.
Step 9: Continue finding n until you get a precise value.
The square root of √1413 is approximately 37.59.
Square Root of 1413 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 1413 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √1413.
The smallest perfect square less than 1413 is 1369, and the largest perfect square greater than 1413 is 1444. √1413 falls somewhere between 37 and 38.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). By the formula, (1413 - 1369) / (1444 - 1369) = 44 / 75 ≈ 0.5867.
Using the formula, we identified the decimal approximation of our square root. The next step is adding the integer value to the decimal number, which is 37 + 0.5867 ≈ 37.59.
So the square root of 1413 is approximately 37.59.
Common Mistakes and How to Avoid Them in the Square Root of 1413
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. Now let us look at a few of these 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 has 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, 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 that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important before moving on to the second step.
For Example: √(12+24) = √12 + √24 is the wrong use of roots. The right way 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 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. This may happen in subtraction or elsewhere.
Square Root of 1413 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1413?
The area of the square is approximately 1994.47 square units.
Explanation
The area of the square = side^2.
The side length is given as √1413.
Area of the square = side^2 = √1413 x √1413 ≈ 37.59 x 37.59 ≈ 1994.47.
Therefore, the area of the square box is approximately 1994.47 square units.
Problem 2
A square-shaped building measuring 1413 square feet is built; if each of the sides is √1413, what will be the square feet of half of the building?
706.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1413 by 2, we get 706.5.
So half of the building measures 706.5 square feet.
Problem 3
Calculate √1413 x 5.
187.95
Explanation
The first step is to find the square root of 1413, which is approximately 37.59.
The second step is to multiply 37.59 by 5.
So 37.59 x 5 ≈ 187.95.
Problem 4
What will be the square root of (1400 + 13)?
The square root is approximately 37.59.
Explanation
To find the square root, we need to find the sum of (1400 + 13). 1400 + 13 = 1413, and then √1413 ≈ 37.59.
Therefore, the square root of (1400 + 13) is approximately ±37.59.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1413 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 175.18 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√1413 + 50) ≈ 2 × (37.59 + 50) ≈ 2 × 87.59 ≈ 175.18 units.
FAQ on Square Root of 1413
1.What is √1413 in its simplest form?
2.Mention the factors of 1413.
3.Calculate the square of 1413.
4.Is 1413 a prime number?
5.1413 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 1413?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 1413?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 1413
- 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 p and q are integers and q is not equal to zero.
- 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 the reason it is also known as the principal square root.
- Factors: Factors are numbers that divide another number without leaving a remainder. For example, factors of 10 are 1, 2, 5, and 10.
- Approximation: Approximation is the process of finding a value that is close enough to the correct value, typically within an acceptable range or error.
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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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