126 LearnersLast updated on May 26th, 2025
Square Root of 5100
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 5100.
What is the Square Root of 5100?
The square root is the inverse of the square of a number. 5100 is not a perfect square. The square root of 5100 is expressed in both radical and exponential form. In the radical form, it is expressed as √5100, whereas (5100)^(1/2) in the exponential form. √5100 ≈ 71.414, 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 5100
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 5100 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 5100 is broken down into its prime factors.
Step 1: Finding the prime factors of 5100
Breaking it down, we get 2 × 2 × 3 × 5 × 5 × 17: 2² × 3¹ × 5² × 17¹
Step 2: Now we found out the prime factors of 5100. The second step is to make pairs of those prime factors. Since 5100 is not a perfect square, therefore the digits of the number can’t be grouped in pairs completely. Thus, calculating √5100 using prime factorization will provide an approximate solution.
Square Root of 5100 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 5100, we need to group it as 00 and 51.
Step 2: Now we need to find n whose square is 49 or less. We can say n as ‘7’ because 7 × 7 is 49, which is lesser than or equal to 51. Now the quotient is 7 and the remainder is 2 after subtracting 49 from 51.
Step 3: Now let us bring down 00, making the new dividend 200. Add the old divisor with the same number 7 + 7, we get 14, which will be our new divisor.
Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 14n as the new divisor, we need to find the value of n.
Step 5: The next step is finding 14n × n ≤ 200. Let us consider n as 1, now 14 × 1 × 1 = 14.
Step 6: Subtract 14 from 200, the difference is 186, and the quotient is 71.
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 18600.
Step 8: Now we need to find the new divisor that is 141 because 1411 × 1 = 1411.
Step 9: Subtracting 1411 from 18600, we get the result 17189.
Step 10: Now the quotient is 71.4
Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values, continue till the remainder is zero.
So the square root of √5100 is 71.41.
Square Root of 5100 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 5100 using the approximation method.
Step 1: Now we have to find the closest perfect square of √5100. The smallest perfect square less than 5100 is 4900, and the largest perfect square greater than 5100 is 5184. √5100 falls somewhere between 70 and 72.
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 (5100 - 4900) ÷ (5184 - 4900) = 200 ÷ 284 = 0.704 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 + 0.704 = 70.704, so the square root of 5100 is approximately 71.414.
Common Mistakes and How to Avoid Them in the Square Root of 5100
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping important 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 typically the required one.
For example: √50 = 7.071, there is also -7.071 which should not be forgotten.
Mistake 2
Not adding 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 and then move on to the second step.
For Example: √(12+24) = √12 + √24 is a 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 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 calculation. This may either happen in subtracting or elsewhere.
Square Root of 5100 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5100?
The area of the square is 5100 square units.
Explanation
The area of the square = side².
The side length is given as √5100.
Area of the square = side² = √5100 × √5100 = 5100.
Therefore, the area of the square box is 5100 square units.
Problem 2
A square-shaped building measuring 5100 square feet is built; if each of the sides is √5100, what will be the square feet of half of the building?
2550 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 5100 by 2, we get 2550.
So half of the building measures 2550 square feet.
Problem 3
Calculate √5100 × 5.
357.07
Explanation
The first step is to find the square root of 5100, which is approximately 71.414.
The second step is to multiply 71.414 with 5.
So 71.414 × 5 ≈ 357.07.
Problem 4
What will be the square root of (5000 + 100)?
The square root is approximately 71.414.
Explanation
To find the square root, we need to find the sum of (5000 + 100). 5000 + 100 = 5100, and then √5100 ≈ 71.414.
Therefore, the square root of (5000 + 100) is approximately ±71.414.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √5100 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 218.828 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√5100 + 38) = 2 × (71.414 + 38) = 2 × 109.414 ≈ 218.828 units.
FAQ on Square Root of 5100
1.What is √5100 in its simplest form?
2.Mention the factors of 5100.
3.Calculate the square of 5100.
4.Is 5100 a prime number?
5.5100 is divisible by?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 5100?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 5100?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for the Square Root of 5100
- Square root: A square root is the inverse of a square. For 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, q is not equal to zero, and p and q are integers.
- Approximation method: A technique used to find an approximate value of a square root, especially for non-perfect squares.
- Long division method: A step-by-step method used to find the square root of non-perfect squares.
- Prime factorization: Breaking down a number into its basic prime factors. For example, the prime factorization of 5100 is 2 × 2 × 3 × 5 × 5 × 17.
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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.
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