117 LearnersLast updated on May 26th, 2025
Square Root of 5161
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 various fields such as engineering, physics, and finance. Here, we will discuss the square root of 5161.
What is the Square Root of 5161?
The square root is the inverse of the square of the number. 5161 is not a perfect square. The square root of 5161 is expressed in both radical and exponential form. In the radical form, it is expressed as √5161, whereas (5161)^(1/2) in the exponential form. √5161 ≈ 71.851, 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 5161
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 5161 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5161 is broken down into its prime factors.
Step 1: Finding the prime factors of 5161
Breaking it down, we get 11 × 469: 11^1 × 469^1
Step 2: Now we found out the prime factors of 5161. Since 5161 is not a perfect square, its digits cannot be grouped in pairs. Therefore, calculating 5161 using prime factorization cannot yield an exact square root.
Square Root of 5161 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 5161, we need to group it as 61 and 51.
Step 2: Now, find n whose square is less than or equal to 51. We can say n is 7 because 7 × 7 = 49, which is lesser than 51. Now the quotient is 7, and the remainder is 51 - 49 = 2.
Step 3: Bring down 61, making the new dividend 261. Add the old divisor with the same number: 7 + 7 = 14, which will be our new divisor's starting digits.
Step 4: Find the largest digit x such that 14x × x ≤ 261. Let us consider x as 1, now 141 × 1 = 141.
Step 5: Subtract 261 from 141; the difference is 120, and the quotient is 71.
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 12000.
Step 7: Find the new divisor: 142, and find a digit x such that 142x × x ≤ 12000.
Step 8: Continuing the process, we get the quotient as approximately 71.85.
So the square root of √5161 is approximately 71.85.
Square Root of 5161 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 5161 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √5161. The smallest perfect square less than 5161 is 4900 (70^2), and the largest perfect square greater than 5161 is 5184 (72^2). √5161 falls somewhere between 70 and 72.
Step 2: Now we apply the formula: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square) (5161 - 4900) ÷ (5184 - 4900) = 261 ÷ 284 ≈ 0.919 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 70 + 0.919 ≈ 70.919, so the approximate square root of 5161 is 71.85.
Common Mistakes and How to Avoid Them in the Square Root of 5161
Students make mistakes while finding square roots, 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 has both positive and negative square roots. However, we typically consider only the principal (positive) square root in practical applications.
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 common mistake. To resolve this, students should understand that simplifying the numbers inside the square root is important before moving on to further steps.
For example: √(12 + 24) = √36 = 6, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
Students should be taught to simplify and accurately approximate values inside the square root to avoid errors.
For example: √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root to avoid confusion.
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. Students may accidentally skip a step, resulting in a wrong answer at the end. This may occur during subtraction or elsewhere in the process.
Square Root of 5161 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5161?
The area of the square is approximately 5161 square units.
Explanation
The area of the square = side^2.
The side length is given as √5161.
Area of the square = (√5161) × (√5161) = 5161.
Therefore, the area of the square box is approximately 5161 square units.
Problem 2
A square-shaped garden measures 5161 square feet. If each of the sides is √5161, what will be the square feet of half of the garden?
2580.5 square feet
Explanation
To find half of the area of the square-shaped garden, simply divide 5161 by 2.
Dividing 5161 by 2 = 2580.5 square feet.
So half of the garden measures 2580.5 square feet.
Problem 3
Calculate √5161 × 3.
Approximately 215.553
Explanation
The first step is to find the square root of 5161, which is approximately 71.85.
The second step is to multiply 71.85 by 3.
So 71.85 × 3 ≈ 215.553.
Problem 4
What will be the square root of (5161 + 39)?
Approximately 72
Explanation
To find the square root, first find the sum of (5161 + 39). 5161 + 39 = 5200, and then √5200 ≈ 72.
Therefore, the square root of (5161 + 39) is approximately 72.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √5161 units and the width ‘w’ is 39 units.
We find the perimeter of the rectangle as approximately 221.702 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√5161 + 39) = 2 × (71.85 + 39) = 2 × 110.85 ≈ 221.702 units.
FAQ on Square Root of 5161
1.What is √5161 in its simplest form?
2.Mention the factors of 5161.
3.Calculate the square of 5161.
4.Is 5161 a prime number?
5.5161 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 5161?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 5161?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 5161
- 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: √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.
- Principal square root: A number has both positive and negative square roots. The principal square root is the positive square root, which is typically used in real-world applications.
- Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it can be expressed as 4 × 4.
- Long division method: A systematic method used to find the square root of non-perfect square numbers by dividing and approximating in steps.
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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
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