125 LearnersLast updated on May 26th, 2025
Square Root of 3225
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 3225.
What is the Square Root of 3225?
The square root is the inverse of the square of the number. 3225 is not a perfect square. The square root of 3225 is expressed in both radical and exponential form. In the radical form, it is expressed as √3225, whereas in the exponential form it is expressed as (3225)^(1/2). √3225 ≈ 56.775, 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 3225
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 3225 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 3225 is broken down into its prime factors.
Step 1: Finding the prime factors of 3225 Breaking it down, we get 3 x 5 x 5 x 43: 3^1 x 5^2 x 43^1
Step 2: Now we found out the prime factors of 3225. The second step is to make pairs of those prime factors. Since 3225 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 3225 using prime factorization is impossible.
Square Root of 3225 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 3225, we need to group it as 32 and 25.
Step 2: Now we need to find n whose square is closest to 32. We can say n as ‘5’ because 5 x 5 = 25 is lesser than 32. Now the quotient is 5 and after subtracting 25 from 32, the remainder is 7.
Step 3: Now let us bring down 25 which is the new dividend. Add the old divisor with the same number 5 + 5 to get 10, which will be our new divisor.
Step 4: The new divisor will be 10n. We need to find the value of n such that 10n x n ≤ 725. Let us consider n as 7, now 107 x 7 = 749, which is more than 725, so n should be less than 7.
Step 5: If n = 6, then 106 x 6 = 636, which fits. Subtracting gives a remainder of 89.
Step 6: Since the dividend is less than the divisor, we need to add a decimal point and add two zeroes to the dividend. Now the new dividend is 8900.
Step 7: Now we need to find the new divisor. Extend the divisor to 1066 and find n such that 1066n x n is close to 8900. Let n = 8, then 10668 x 8 = 85344, which is an overestimate, thus n should be less than 8.
Step 8: Try n = 7, then 10667 x 7 = 74669, which fits. Subtracting gives a remainder of 1431.
Step 9: Continue doing these steps until we get two numbers after the decimal point. For example, the result will approximate to 56.77. So the square root of √3225 is approximately 56.77.
Square Root of 3225 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 3225 using the approximation method.
Step 1: Now we have to find the closest perfect squares to √3225. The closest perfect square less than 3225 is 3136 (56^2) and the closest perfect square greater than 3225 is 3364 (58^2). √3225 falls somewhere between 56 and 58.
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 (3225 - 3136) ÷ (3364 - 3136) = 89 ÷ 228 ≈ 0.39035. 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 56 + 0.39 ≈ 56.39. Therefore, the square root of 3225 is approximately 56.39.
Common Mistakes and How to Avoid Them in the Square Root of 3225
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division methods, etc. 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 the required one.
For example: √50 ≈ 7.07, there is also -7.07 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root 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 the 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 ≈ 7.071067.
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 sum. This may either happen in subtracting or elsewhere.
Square root of 3225 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √3225?
The area of the square is approximately 3225 square units.
Explanation
The area of the square = side^2.
The side length is given as √3225.
Area of the square = side^2 = √3225 x √3225 = 3225.
Therefore, the area of the square box is approximately 3225 square units.
Problem 2
A square-shaped building measuring 3225 square feet is built; if each of the sides is √3225, what will be the square feet of half of the building?
1612.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 3225 by 2 = 1612.5.
So half of the building measures 1612.5 square feet.
Problem 3
Calculate √3225 x 5.
Approximately 283.875
Explanation
The first step is to find the square root of 3225, which is approximately 56.775.
The second step is to multiply 56.775 with 5.
So 56.775 x 5 ≈ 283.875.
Problem 4
What will be the square root of (3225 + 25)?
The square root is approximately 57.
Explanation
To find the square root, we need to find the sum of (3225 + 25).
3225 + 25 = 3250, and then √3250 ≈ 57.
Therefore, the square root of (3225 + 25) is approximately ±57.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √3225 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as approximately 189.55 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√3225 + 38) ≈ 2 × (56.775 + 38) ≈ 2 × 94.775 ≈ 189.55 units.
FAQ on Square Root of 3225
1.What is √3225 in its simplest form?
2.Mention the factors of 3225.
3.Calculate the square of 3225.
4.Is 3225 a prime number?
5.3225 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 3225?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 3225?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 3225
- Square root: A square root is the inverse of a square. Example: 4^2 = 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, 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; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
- Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.
- Perfect square: A perfect square is an integer that is the square of another integer. For example, 9 is a perfect square because it is 3^2.
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About BrightChamps in Qatar
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.
