139 LearnersLast updated on May 26th, 2025
Square Root of 4046
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, finance, etc. Here, we will discuss the square root of 4046.
What is the Square Root of 4046?
The square root is the inverse of the square of a number. 4046 is not a perfect square. The square root of 4046 is expressed in both radical and exponential form. In the radical form, it is expressed as √4046, whereas in exponential form it is (4046)^(1/2). √4046 ≈ 63.593, 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 4046
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where 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 4046 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 4046 is broken down into its prime factors:
Step 1: Finding the prime factors of 4046 Breaking it down, we get 2 x 2023. 2023 is further factorized as 7 x 17 x 17.
Step 2: Now we found out the prime factors of 4046. The second step is to make pairs of those prime factors. Since 4046 is not a perfect square, the digits of the number can’t be perfectly grouped in pairs.
Therefore, calculating 4046 using prime factorization does not yield an exact value.
Square Root of 4046 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 4046, we need to group it as 46 and 40.
Step 2: Now we need to find n whose square is 40. We can say n as ‘6’ because 6 x 6 = 36 is lesser than or equal to 40. Now the quotient is 6; after subtracting 36 from 40, the remainder is 4.
Step 3: Now let us bring down 46, which is the new dividend. Add the old divisor with the same number 6 + 6 we get 12, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 12n × n ≤ 446. Let us consider n as 3, now 12 x 3 x 3 = 369.
Step 6: Subtract 369 from 446, the difference is 77, and the quotient is 63.
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 7700.
Step 8: Now we need to find the new divisor that is 635 because 635 x 5 = 3175.
Step 9: Subtracting 3175 from 7700, we get the result 4525.
Step 10: Now the quotient is 63.5.
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.
So the square root of √4046 is approximately 63.59.
Square Root of 4046 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 4046 using the approximation method.
Step 1: Now we have to find the closest perfect square of √4046. The smallest perfect square less than 4046 is 3969 (63^2), and the largest perfect square greater than 4046 is 4096 (64^2). √4046 falls somewhere between 63 and 64.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (4046 - 3969) ÷ (4096 - 3969) = 77 ÷ 127 = 0.606. 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 63 + 0.606 = 63.606. So the square root of 4046 is approximately 63.606.
Common Mistakes and How to Avoid Them in the Square Root of 4046
Students do 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 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 the 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 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 of the sum. This may happen in subtracting or elsewhere.
Square Root of 4046 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √4046?
The area of the square is approximately 163,696 square units.
Explanation
The area of the square = side^2.
The side length is given as √4046.
Area of the square = side^2 = √4046 × √4046 = 4046.
Therefore, the area of the square box is 4046 square units.
Problem 2
A square-shaped building measuring 4046 square feet is built; if each of the sides is √4046, what will be the square feet of half of the building?
2023 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 4046 by 2, we get 2023.
So half of the building measures 2023 square feet.
Problem 3
Calculate √4046 × 5.
Approximately 317.965.
Explanation
The first step is to find the square root of 4046, which is approximately 63.593.
The second step is to multiply 63.593 with 5.
So 63.593 × 5 = 317.965.
Problem 4
What will be the square root of (4040 + 6)?
The square root is approximately 63.593.
Explanation
To find the square root, we need to find the sum of 4040 + 6.
4040 + 6 = 4046, and then √4046 ≈ 63.593.
Therefore, the square root of (4040 + 6) is approximately ±63.593.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √4046 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 227.186 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√4046 + 50)
= 2 × (63.593 + 50)
= 2 × 113.593
= 227.186 units.
FAQ on Square Root of 4046
1.What is √4046 in its simplest form?
2.Mention the factors of 4046.
3.Calculate the square of 4046.
4.Is 4046 a prime number?
5.4046 is divisible by?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 4046?
8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 4046?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for the Square Root of 4046
- Square root: A square root is the inverse of a square. For example, 8^2 = 64, and the inverse of the square is the square root, which is √64 = 8.
- 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 the positive square root that has more prominence due to its uses in the real world. That is why it is also known as the principal square root.
- Prime factorization: Prime factorization involves breaking down a number into its smallest prime factors.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 64 is a perfect square because it is 8^2.
Explore More algebra
About BrightChamps in Philippines
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.
