125 LearnersLast updated on May 26th, 2025
Square Root of 3125
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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 3125.
What is the Square Root of 3125?
The square root is the inverse of the square of the number. 3125 is not a perfect square. The square root of 3125 is expressed in both radical and exponential form. In the radical form, it is expressed as √3125, whereas (3125)^(1/2) in the exponential form. √3125 ≈ 55.9017, 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 3125
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 3125 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3125 is broken down into its prime factors.
Step 1: Finding the prime factors of 3125 Breaking it down, we get 5 x 5 x 5 x 5 x 5: 5^5
Step 2: Now we found out the prime factors of 3125. The second step is to make pairs of those prime factors. Since 3125 is not a perfect square, the digits of the number can’t be grouped entirely in pairs. Therefore, calculating the square root of 3125 using prime factorization involves simplifying it to √(5^2 × 5^2 × 5) = 25√5.
Square Root of 3125 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 3125, we need to group it as 31 and 25.
Step 2: Now we need to find n whose square is less than or equal to 31. We can say n is '5' because 5^2 = 25 is less than 31. Now the quotient is 5, after subtracting 31-25, the remainder is 6.
Step 3: Now let us bring down 25, making the new dividend 625. Add the old divisor (5) with the same number to get 10, which will be our new divisor (5 becomes 50 when we double it as part of the calculation).
Step 4: The new divisor will be 10n; we need to find the value of n such that 10n x n ≤ 625. Choosing n as 5 works because 105 x 5 = 525.
Step 5: Subtract 525 from 625; the difference is 100, and the quotient is 55.
Step 6: Since the new dividend (100) is less than the new divisor (105), 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 10000.
Step 7: Now we need to find the new divisor, which will be 110n, where n = 9. Because 1109 ✖ 9 = 9981, which is close to 10000.
Step 8: Subtracting 9981 from 10000 gives us 19.
Step 9: Continue doing these steps until we achieve sufficient precision. So the square root of √3125 is approximately 55.9017.
Square Root of 3125 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 3125 using the approximation method.
Step 1: We need to find the closest perfect squares of √3125. The smallest perfect square below 3125 is 3025 (which is 55^2), and the largest perfect square above 3125 is 3136 (which is 56^2). √3125 falls somewhere between 55 and 56.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (3125 - 3025) / (3136 - 3025) = 100 / 111 ≈ 0.9009. Adding this value to the integer part gives us approximately 55.9009. Therefore, the square root of 3125 is approximately 55.9017.
Common Mistakes and How to Avoid Them in the Square Root of 3125
Students do make mistakes while finding square roots, such as forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important for students to understand that a number has both positive and negative square roots. However, we usually consider only the positive square root, as it is the most relevant in real-world applications.
For example: √3125 ≈ 55.9017, but there is also -55.9017, which should not be ignored in some contexts.
Mistake 2
Not adding square root symbol in proper places
Not using the square root symbol correctly is another common mistake. Students should simplify the numbers inside the square root first before proceeding.
For example: √(100 + 225) = √325 is correct, not √100 + √225 = 10 + 15 = 25.
Mistake 3
Not finding the correct value of a non-perfect square
Students should simplify and approximate the square root of non-perfect squares accurately.
For example: √50 ≈ 7.071 is the correct approximation, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to distinguish between the square root and cube root symbols.
For example: √50 and ∛50 are different operations and should not be confused.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves multiple steps. Students might skip steps accidentally, leading to incorrect results. It is crucial to follow each step carefully to avoid errors.
Square Root of 3125 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3125?
The area of the square is 3125 square units.
Explanation
The area of the square = side^2.
The side length is given as √3125.
Area of the square = side^2 = √3125 × √3125 = 3125.
Therefore, the area of the square box is 3125 square units.
Problem 2
A square-shaped field measuring 3125 square feet is built; if each of the sides is √3125, what will be the square feet of half of the field?
1562.5 square feet
Explanation
We can divide the given area by 2 as the field is square-shaped.
Dividing 3125 by 2 = we get 1562.5.
So half of the field measures 1562.5 square feet.
Problem 3
Calculate √3125 × 3.
167.7051
Explanation
The first step is to find the square root of 3125, which is approximately 55.9017.
The second step is to multiply 55.9017 by 3.
So 55.9017 × 3 ≈ 167.7051.
Problem 4
What will be the square root of (3125 + 25)?
The square root is approximately 56.7005.
Explanation
To find the square root, we need to find the sum of (3125 + 25). 3125 + 25 = 3150, and then √3150 ≈ 56.7005.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √3125 units and the width 'w' is 50 units.
The perimeter of the rectangle is approximately 211.8034 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3125 + 50) ≈ 2 × (55.9017 + 50) ≈ 2 × 105.9017 ≈ 211.8034 units.
FAQ on Square Root of 3125
1.What is √3125 in its simplest form?
2.Mention the factors of 3125.
3.Calculate the square of 3125.
4.Is 3125 a prime number?
5.3125 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 3125?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 3125?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 3125
- Square root: A square root is the inverse of a square. Example: 4^2 = 16 and the inverse 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, but the positive square root is usually more relevant in real-world applications.
- Prime factorization: Breaking down a number into its basic prime number components. For example, the prime factorization of 3125 is 5^5.
- Long division method: A technique for finding square roots of numbers that are not perfect squares by dividing and averaging.
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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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