121 LearnersLast updated on May 26th, 2025
Square Root of 1225
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 1225.
What is the Square Root of 1225?
The square root is the inverse of the square of the number. 1225 is a perfect square. The square root of 1225 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1225, whereas (1225)^(1/2) in the exponential form. √1225 = 35, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 1225
The prime factorization method is typically used for perfect square numbers like 1225. The long division method and approximation method are more suited for non-perfect square numbers. Let us now learn the following method:
Prime factorization method
Square Root of 1225 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 1225 is broken down into its prime factors.
Step 1: Finding the prime factors of 1225 Breaking it down, we get 5 x 5 x 7 x 7: 5^2 x 7^2 Step 2: Now we found out the prime factors of 1225. The second step is to make pairs of those prime factors. Since 1225 is a perfect square, the digits of the number can be grouped into pairs.
Therefore, calculating √1225 using prime factorization gives us 5 x 7 = 35.
Square Root of 1225 by Long Division Method
The long division method is generally used for non-perfect square numbers but can be demonstrated for perfect squares like 1225 for practice. In this method, we verify that our calculation matches the known perfect square root.
Step 1: To begin with, we need to group the numbers from right to left. In the case of 1225, we need to group it as 12 and 25.
Step 2: Now we need to find n whose square is less than or equal to 12. We can say n is ‘3’ because 3 x 3 = 9 is less than 12. Now the quotient is 3, and after subtracting 9 from 12, the remainder is 3.
Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor with the same number, 3 + 3 = 6, which will be our new divisor.
Step 4: The next step is finding 6n x n ≤ 325. Let us consider n as 5; now 65 x 5 = 325.
Step 5: Subtract 325 from 325, and the remainder is 0. The quotient is 35.
Step 6: Since the remainder is 0, we can conclude that √1225 = 35.
Square Root of 1225 by Approximation Method
The approximation method is not necessary for 1225 as it is a perfect square, but it can be used to verify the calculation.
Step 1: We find the closest perfect square to 1225, which are 1225 itself or nearby perfect squares.
Step 2: Since 1225 is a perfect square, √1225 directly gives us an integer value, which is 35.
Common Mistakes and How to Avoid Them in the Square Root of 1225
Students make mistakes while finding square roots, such as forgetting about the negative square root or skipping prime factorization steps. Let us look at a few common mistakes 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 usually consider only the positive square root in practical scenarios.
For example: √1225 = 35, there is also -35 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 mistake students make. To resolve this, we need to teach students that simplifying numbers inside the square root is important before proceeding.
For Example: √(25 + 100) = √125, not √25 + √100.
Mistake 3
Not finding the correct value of a non-perfect square
For non-perfect squares, students should practice methods such as the long division or approximation to ensure accuracy.
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: √125 and ∛125 are different.
Mistake 5
Skipping steps in prime factorization
Finding a square root using the prime factorization method involves several steps. Skipping steps can lead to incorrect answers. Students should practice breaking down numbers into their prime factors correctly.
Square root of 1225 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √1024?
The area of the square is 1024 square units.
Explanation
The area of the square = side^2.
The side length is given as √1024.
Area of the square = side^2 = √1024 x √1024 = 32 × 32 = 1024.
Therefore, the area of the square box is 1024 square units.
Problem 2
A square-shaped building measuring 1225 square feet is built; if each of the sides is √1225, what will be the square feet of half of the building?
612.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 1225 by 2 = we get 612.5.
So half of the building measures 612.5 square feet.
Problem 3
Calculate √1225 x 4.
140
Explanation
The first step is to find the square root of 1225, which is 35.
The second step is to multiply 35 by 4.
So 35 x 4 = 140.
Problem 4
What will be the square root of (625 + 600)?
The square root is 35.
Explanation
To find the square root, we need to find the sum of (625 + 600).
625 + 600 = 1225, and then √1225 = 35.
Therefore, the square root of (625 + 600) is ±35.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √1225 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is 170 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√1225 + 50)
= 2 × (35 + 50)
= 2 × 85
= 170 units.
FAQ on Square Root of 1225
1.What is √1225 in its simplest form?
2.Mention the factors of 1225.
3.Calculate the square of 35.
4.Is 1225 a prime number?
5.1225 is divisible by?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 1225?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 1225?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 1225
- Square root: A square root is the inverse of a square. Example: 6^2 = 36, and the inverse of the square is the square root, that is √36 = 6.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. For example: 36, 49, 64, etc.
- Prime factorization: Prime factorization is expressing a number as the product of its prime numbers.
- Integer: An integer is a whole number that can be positive, negative, or zero. Examples include -5, -4, 0, 1, 2, etc.
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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
: He loves to play the quiz with kids through algebra to make kids love it.
