106 LearnersLast updated on May 26th, 2025
Square Root of 10625
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 10625.
What is the Square Root of 10625?
The square root is the inverse of the square of a number. 10625 is a perfect square. The square root of 10625 is expressed in both radical and exponential form. In the radical form, it is expressed as √10625, whereas (10625)^(1/2) in the exponential form. √10625 = 103, 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 10625
The prime factorization method is used for perfect square numbers. Let us now learn the following methods:
- Prime factorization method
- Long division method
Square Root of 10625 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 10625 is broken down into its prime factors.
Step 1: Finding the prime factors of 10625
Breaking it down, we get 5 x 5 x 5 x 5 x 17: 5^4 x 17^1
Step 2: Now that we found out the prime factors of 10625, the second step is to make pairs of those prime factors. Since 10625 is a perfect square, prime factors can be paired: (5 x 5), (5 x 5). Therefore, calculating 10625 using prime factorization gives us 103.
Square Root of 10625 by Long Division Method
The long division method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. 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 10625, we group it as 25 and 106.
Step 2: Now, we need to find n whose square is less than or equal to 106. We can say n is ‘10’ because 10 x 10 = 100, which is less than 106. Now the quotient is 10, after subtracting 106 - 100, the remainder is 6.
Step 3: Bring down 25 to make the new dividend 625.
Step 4: The new divisor will be the sum of the old divisor and the quotient, so 10 + 10 = 20.
Step 5: We need to find n such that 20n x n ≤ 625. Let us consider n as 3. Now, 203 x 3 = 609.
Step 6: Subtract 625 from 609, the difference is 16, and the quotient is 103.
Step 7: Since there is no remainder, the process stops here, confirming that the square root of 10625 is 103.
Square Root of 10625 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √10625?
The area of the square is 10625 square units.
Explanation
The area of the square = side^2.
The side length is given as √10625.
Area of the square = side^2 = √10625 x √10625 = 103 x 103 = 10625
Therefore, the area of the square box is 10625 square units.
Problem 2
A square-shaped building measuring 10625 square feet is built; if each of the sides is √10625, what will be the square feet of half of the building?
5312.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 10625 by 2 = we get 5312.5
So half of the building measures 5312.5 square feet.
Problem 3
Calculate √10625 x 5.
515
Explanation
The first step is to find the square root of 10625, which is 103.
The second step is to multiply 103 by 5.
So 103 x 5 = 515.
Problem 4
What will be the square root of (10000 + 625)?
The square root is 103
Explanation
To find the square root, we need to find the sum of (10000 + 625). 10000 + 625 = 10625, and then √10625 = 103.
Therefore, the square root of (10000 + 625) is ±103.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √10625 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 282 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√10625 + 38) = 2 × (103 + 38) = 2 × 141 = 282 units.
FAQ on Square Root of 10625
1.What is √10625 in its simplest form?
2.Mention the factors of 10625.
3.Calculate the square of 10625.
4.Is 10625 a prime number?
5.10625 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 10625?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 10625?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 10625
- 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.
- 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, 4, 9, and 16 are perfect squares.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors.
- Long division method: A systematic method to find the square root of a number, especially useful for large numbers or non-perfect squares.
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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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