100 LearnersLast updated on May 26th, 2025
Square Root of 46.17
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 46.17.
What is the Square Root of 46.17?
The square root is the inverse of the square of the number. 46.17 is not a perfect square. The square root of 46.17 is expressed in both radical and exponential form.
In the radical form, it is expressed as √46.17, whereas (46.17)^(1/2) in the exponential form. √46.17 ≈ 6.794, 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 46.17
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 46.17 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. However, since 46.17 is not a perfect square, calculating its square root using prime factorization is not feasible. We need to resort to methods like long division or approximation for such non-perfect square numbers.
Square Root of 46.17 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 46.17, we need to group it as 46 and 17.
Step 2: Now we need to find n whose square is 4. We can say n as ‘2’ because 2 x 2 is less than or equal to 4. Now the quotient is 2, and after subtracting 4-4, the remainder is 0.
Step 3: Now let us bring down 617 (from 46.17) which is the new dividend. Add the old divisor with the same number, 2 + 2, we get 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find an n such that 4n × n ≤ 617. Let's consider n as 6, so 46 x 6 = 276.
Step 5: Subtract 276 from 617, the difference is 341, and the quotient is now 26.
Step 6: 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 34100.
Step 7: Now we need to find the new divisor that is 539 because 539 x 6 = 3234.
Step 8: Subtracting 3234 from 3410 gives us a remainder of 176.
Step 9: Now the quotient is 6.79.
Step 10: Continue doing these steps until we get the desired precision after the decimal point or until the remainder is zero.
So the square root of √46.17 is approximately 6.794.
Square Root of 46.17 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 46.17 using the approximation method.
Step 1: Now we have to find the closest perfect square to √46.17. The smallest perfect square less than 46.17 is 36 and the largest perfect square greater than 46.17 is 49. √46.17 falls somewhere between 6 and 7.
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 (46.17 - 36) / (49 - 36) = 0.782. 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 6 + 0.782 = 6.782, so the square root of 46.17 is approximately 6.794.
Common Mistakes and How to Avoid Them in the Square Root of 46.17
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. 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.
Square root of 46.17 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √46.17?
The area of the square is approximately 46.17 square units.
Explanation
The area of the square = side².
The side length is given as √46.17.
Area of the square = side² = √46.17 x √46.17 = 46.17.
Therefore, the area of the square box is approximately 46.17 square units.
Problem 2
A square-shaped building measuring 46.17 square feet is built; if each of the sides is √46.17, what will be the square feet of half of the building?
23.085 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 46.17 by 2 gives us 23.085.
So half of the building measures 23.085 square feet.
Problem 3
Calculate √46.17 x 5.
Approximately 33.97
Explanation
The first step is to find the square root of 46.17, which is approximately 6.794.
The second step is to multiply 6.794 by 5.
So 6.794 x 5 ≈ 33.97.
Problem 4
What will be the square root of (46.17 + 3.83)?
The square root is 7
Explanation
To find the square root, we need to find the sum of (46.17 + 3.83). 46.17 + 3.83 = 50.
Therefore, the square root of 50 is approximately ±7.071067, but when approximating to the nearest whole number, it is 7.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √46.17 units and the width ‘w’ is 20 units.
We find the perimeter of the rectangle as approximately 53.588 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√46.17 + 20) ≈ 2 × (6.794 + 20) ≈ 2 × 26.794 ≈ 53.588 units.
FAQ on Square Root of 46.17
1.What is √46.17 in its simplest form?
2.Mention the factors of 46.17.
3.Calculate the square of 46.17.
4.Is 46.17 a prime number?
5.Is 46.17 a perfect square?
Important Glossaries for the Square Root of 46.17
- 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 is not equal to zero and p and q are integers.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Approximation: The process of finding a value that is close enough to the right answer, usually within a specified range.
- Long Division Method: A step-by-step method for calculating the square root of a number that involves dividing and averaging.
Explore More algebra
Previous to Square Root of 46.17
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.
