121 LearnersLast updated on May 26th, 2025
Square Root of 6625
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 6625.
What is the Square Root of 6625?
The square root is the inverse of the square of the number. 6625 is not a perfect square. The square root of 6625 is expressed in both radical and exponential form. In the radical form, it is expressed as √6625, whereas (6625)^(1/2) in the exponential form. √6625 ≈ 81.414, 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 6625
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 and approximation methods are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 6625 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6625 is broken down into its prime factors.
Step 1: Finding the prime factors of 6625. Breaking it down, we get 5 x 5 x 265: 5^2 x 53.
Step 2: Now we found out the prime factors of 6625. The second step is to make pairs of those prime factors. Since 6625 is not a perfect square, therefore, the digits of the number can’t be grouped in pairs.
Therefore, calculating 6625 using prime factorization is impossible.
Square Root of 6625 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 6625, we need to group it as 65 and 6.
Step 2: Now we need to find n whose square is less than or equal to 6. We can say n as '2' because 2 x 2 is 4, which is less than 6. Now the quotient is 2, and after subtracting 4 from 6, the remainder is 2.
Step 3: Now let us bring down 625, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.
Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 2625.
Step 5: The next step is finding 4n x n ≤ 2625. Let us consider n as 6; now, 46 x 6 = 276.
Step 6: Subtract 276 from 2625, and the difference is 2349. The new quotient is 26.
Step 7: Since the dividend is less than the new product, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 234900.
Step 8: Now we need to find the new number n, such that 526n x n is close to 234900. Let's assume n = 4. Then 5264 x 4 ≈ 21056.
Step 9: Subtracting 21056 from 234900, we get the result 22444.
Step 10: Now the quotient is 81.4.
Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.
So the square root of √6625 ≈ 81.41.
Square Root of 6625 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 6625 using the approximation method.
Step 1: Now we have to find the closest perfect square of √6625.
The smallest perfect square less than 6625 is 6561 (81^2), and the largest perfect square greater than 6625 is 6724 (82^2). √6625 falls somewhere between 81 and 82.
Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (6625 - 6561) / (6724 - 6561) = 64 / 163 ≈ 0.393.
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 81 + 0.393 = 81.393, so the square root of 6625 is approximately 81.393.
Common Mistakes and How to Avoid Them in the Square Root of 6625
Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping 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 the required one.
For example: √625 = 25, there is also -25 which should not be forgotten.
Mistake 2
Not adding the 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: √(9+16) ≠ √9 + √16. The right way of using roots is √(9+16) = √25.
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, 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 the 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 6625 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √625?
The area of the square is 625 square units.
Explanation
The area of the square = side^2.
The side length is given as √625.
Area of the square = side^2 = √625 x √625 = 25 x 25 = 625.
Therefore, the area of the square box is 625 square units.
Problem 2
A square-shaped building measuring 6625 square feet is built; if each of the sides is √6625, what will be the square feet of half of the building?
3312.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 6625 by 2 = 3312.5.
So half of the building measures 3312.5 square feet.
Problem 3
Calculate √6625 x 5.
407.07
Explanation
The first step is to find the square root of 6625, which is approximately 81.41.
The second step is to multiply 81.41 by 5.
So 81.41 x 5 = 407.07.
Problem 4
What will be the square root of (625 + 100)?
The square root is 25.
Explanation
To find the square root, we need to find the sum of (625 + 100). 625 + 100 = 725, and then √725 ≈ 26.925.
Therefore, the square root of (625 + 100) is approximately 26.925.
Problem 5
Find the perimeter of the rectangle if its length 'l' is √625 units and the width 'w' is 38 units.
We find the perimeter of the rectangle as 126 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√625 + 38) = 2 × (25 + 38) = 2 × 63 = 126 units.
FAQ on Square Root of 6625
1.What is √6625 in its simplest form?
2.Mention the factors of 6625.
3.Calculate the square of 6625.
4.Is 6625 a prime number?
5.6625 is divisible by?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 6625?
8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 6625?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for the Square Root of 6625
- 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.
- Prime factorization: This is the process of expressing a number as the product of its prime factors.
- Long division method: A systematic method used to find the square root of numbers, especially non-perfect squares, through a series of division steps.
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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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