131 LearnersLast updated on May 26th, 2025
Square Root of 5025
If a number is multiplied by itself, the result is a square. The inverse of the square is the square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 5025.
What is the Square Root of 5025?
The square root is the inverse operation of squaring a number. 5025 is not a perfect square. The square root of 5025 can be expressed in both radical and exponential forms. In the radical form, it is expressed as √5025, whereas in exponential form it is expressed as (5025)^(1/2). √5025 ≈ 70.882, 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 5025
The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers, methods such as long division and approximation are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 5025 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let's look at how 5025 breaks down into its prime factors:
Step 1: Finding the prime factors of 5025
Breaking it down, we get 3 x 3 x 5 x 5 x 67: 3^2 x 5^2 x 67
Step 2: The prime factors of 5025 include pairs of 3 and 5. Since 5025 is not a perfect square, we cannot group all prime factors into pairs. Therefore, calculating √5025 using prime factorization is not straightforward.
Square Root of 5025 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's learn how to find the square root using the long division method, step by step:
Step 1: Start by grouping the numbers from right to left. For 5025, group it as 50 and 25.
Step 2: Find n whose square is less than or equal to 50. Here, n is 7 because 7 x 7 = 49, which is less than 50. Subtract 49 from 50 to get a remainder of 1, and bring down 25, making the new dividend 125.
Step 3: Double the quotient (7) to get 14, which becomes part of our new divisor.
Step 4: Find a digit x such that 14x times x is less than or equal to 125. Here, x is 8 because 148 times 8 = 1184, which is less than 1250. Subtract 1184 from 1250 to get a remainder of 66.
Step 5: Continue the process by bringing down pairs of zeros and repeating the steps to find the next digits. Eventually, you'll approximate √5025 to 70.882.
Square Root of 5025 by Approximation Method
The approximation method is another way to find square roots. It is an easy method to estimate the square root of a given number. Here's how to find the square root of 5025 using the approximation method:
Step 1: Identify the closest perfect squares around 5025. The smallest perfect square less than 5025 is 4900 (70^2), and the largest perfect square greater than 5025 is 5184 (72^2). So, √5025 falls between 70 and 72.
Step 2: Apply linear interpolation: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (5025 - 4900) / (5184 - 4900) = 125 / 284 Using this, √5025 is approximately 70.882.
Common Mistakes and How to Avoid Them in Finding the Square Root of 5025
Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Let's review some common mistakes in detail.
Mistake 1
Forgetting about the Negative Square Root
Students should be aware that a number has both positive and negative square roots. However, we usually consider only the positive square root, as it is typically required for practical purposes.
For example: √5025 ≈ 70.882, but -70.882 is also a valid square root.
Mistake 2
Not Adding the Square Root Symbol in Proper Places
Incorrect use of the square root symbol is a common error. It is important to simplify numbers inside the square root before proceeding.
For example: √(25 + 100) = √125 is incorrect if simplified as √25 + √100.
The correct expression is √125.
Mistake 3
Not Finding the Correct Value of a Non-Perfect Square
Students should simplify numbers inside the square root first to avoid errors in approximation.
For example: √5025 ≈ 71 is incorrect, while √5025 ≈ 70.882 is correct.
Mistake 4
Confusing the Square Root Symbol with the Cube Root
It's crucial to distinguish between square roots and cube roots.
For example: √5025 and ∛5025 are different and should not be confused.
Mistake 5
Making Mistakes in Long Division
Finding a square root using the Long Division method involves multiple steps, which can lead to errors if steps are skipped or miscalculated. It is important to carefully follow each step to ensure accuracy.
Square Root of 5025 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √5025?
The area of the square is 5025 square units.
Explanation
The area of a square is calculated as side^2.
Given the side length as √5025: Area = (√5025) x (√5025) = 5025 square units.
Problem 2
A square-shaped building measuring 5025 square feet is built; if each side is √5025, what will be the square feet of half of the building?
2512.5 square feet
Explanation
Divide the total area by 2 to find half of the building's area: 5025 / 2 = 2512.5 square feet
Problem 3
Calculate √5025 x 5.
354.41
Explanation
First, find the square root of 5025, which is approximately 70.882.
Then multiply by 5: 70.882 x 5 ≈ 354.41
Problem 4
What will be the square root of (2500 + 25)?
The square root is 50.5
Explanation
To find the square root, sum (2500 + 25) = 2525, then calculate the square root: √2525 ≈ 50.5
Problem 5
Find the perimeter of the rectangle if its length 'l' is √5025 units and the width 'w' is 25 units.
The perimeter of the rectangle is approximately 191.764 units.
Explanation
Perimeter of a rectangle = 2 × (length + width):
Perimeter = 2 × (√5025 + 25) = 2 × (70.882 + 25) ≈ 191.764 units.
FAQ on Square Root of 5025
1.What is √5025 in its simplest form?
2.Mention the factors of 5025.
3.Calculate the square of 5025.
4.Is 5025 a prime number?
5.5025 is divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 5025?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 5025?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossary for the Square Root of 5025
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: The square root of 16 is 4 because 4 x 4 = 16.
- Irrational number: An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion.
- Principal square root: The principal square root is the positive square root of a number. It is the most commonly used in practical applications.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors.
- Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, such as 7.86 or 8.65.
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About BrightChamps in Vietnam
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.
