126 LearnersLast updated on May 26th, 2025
Square Root of 6425
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 6425.
What is the Square Root of 6425?
The square root is the inverse of the square of the number. 6425 is not a perfect square. The square root of 6425 is expressed in both radical and exponential form. In the radical form, it is expressed as √6425, whereas (6425)^(1/2) in the exponential form. √6425 ≈ 80.156, 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 6425
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 6425 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 6425 is broken down into its prime factors.
Step 1: Finding the prime factors of 6425 Breaking it down, we get 5 x 5 x 257 = 5² x 257
Step 2: Now we found out the prime factors of 6425. The second step is to make pairs of those prime factors. Since 6425 is not a perfect square, the digits of the number can’t be grouped into pairs.
Therefore, calculating 6425 using prime factorization is impossible.
Square Root of 6425 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 6425, we need to group it as 25 and 64.
Step 2: Now we need to find n whose square is less than or equal to 64. We can say n is 8 because 8 x 8 = 64. Now the quotient is 8 after subtracting 64 from 64, the remainder is 0.
Step 3: Now let us bring down 25, which is the new dividend. Add the old divisor with the same number, 8 + 8, to get 16, which will be our new divisor.
Step 4: The new divisor will be combined with a digit 'n'. Now we get 16n, and we need to find the value of n such that 16n x n ≤ 25.
Step 5: Considering n as 1, we have 161 x 1 = 161, which is greater than 25. Therefore, we place a decimal point and add two zeroes to the dividend to make it 2500.
Step 6: Now we find the new divisor. With 161, we find n such that 161n x n ≤ 2500. Trying n = 5, we get 1615 x 5 = 8075, which is still greater than 2500.
Step 7: Trying n = 0, we place the decimal point and continue with the same steps to further calculate the square root up to the desired decimal places.
So the square root of √6425 is approximately 80.156.
Square Root of 6425 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 6425 using the approximation method.
Step 1: Identify the closest perfect squares of 6425.
The smallest perfect square less than 6425 is 6400 (80²), and the largest perfect square greater than 6425 is 6561 (81²). √6425 falls somewhere between 80 and 81.
Step 2: Apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). (6425 - 6400) / (6561 - 6400) ≈ 0.156
Using the formula, we identified the decimal increment to add to 80, the initial approximation, resulting in 80 + 0.156 = 80.156.
Thus, the square root of 6425 is approximately 80.156.
Common Mistakes and How to Avoid Them in the Square Root of 6425
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps. Now 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 does have both positive and negative square roots. However, we will be taking only the principal (positive) square root in most practical applications.
For example, √50 = 7.07, but there is also -7.07, 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 that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important before moving on.
For example: √(12 + 24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught 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 ≈ 7.071, 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 consistently, 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, students might skip a step accidentally, leading to an incorrect answer. This may occur during subtraction or other steps.
Square root of 6425 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √6425?
The area of the square is 6425 square units.
Explanation
The area of the square = side².
The side length is given as √6425.
Area of the square = side² = √6425 x √6425 = 6425.
Therefore, the area of the square box is 6425 square units.
Problem 2
A square-shaped building measuring 6425 square feet is built; if each of the sides is √6425, what will be the square feet of half of the building?
3212.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 6425 by 2 = 3212.5.
So half of the building measures 3212.5 square feet.
Problem 3
Calculate √6425 x 5.
400.78
Explanation
The first step is to find the square root of 6425, which is approximately 80.156.
The second step is to multiply 80.156 by 5.
So 80.156 x 5 ≈ 400.78.
Problem 4
What will be the square root of (6400 + 25)?
The square root is 81.
Explanation
To find the square root, we need to find the sum of (6400 + 25). 6400 + 25 = 6425, and then √6425 ≈ 80.156. However, if the numbers were perfect squares, like (6400 + 161), that would have resulted in a perfect square.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √6425 units and the width ‘w’ is 30 units.
The perimeter of the rectangle is 220.312 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√6425 + 30) = 2 × (80.156 + 30) = 2 × 110.156 = 220.312 units.
FAQ on Square Root of 6425
1.What is √6425 in its simplest form?
2.Mention the factors of 6425.
3.Calculate the square of 6425.
4.Is 6425 a prime number?
5.6425 is divisible by?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 6425?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 6425?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for the Square Root of 6425
- Square root: A square root is the inverse of a square. For example, 4²=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, but the positive square root has more prominence due to its uses in the real world. This is known as the principal square root.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 6425 is 5² x 257.
- Decimal point: The dot used to separate the whole part from the fractional part of a number. For example, in 80.156, the decimal point separates 80 from 156.
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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.
