114 LearnersLast updated on May 26th, 2025
Square Root of 10.25
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 10.25.
What is the Square Root of 10.25?
The square root is the inverse of the square of the number. 10.25 is a perfect square. The square root of 10.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √10.25, whereas (10.25)^(1/2) in the exponential form. √10.25 = 3.2, 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 10.25
The prime factorization method is used for perfect square numbers. However, for decimal perfect squares, the long-division method and approximation method are used. Let us now learn the following methods:
- Long division method
- Approximation method
Square Root of 10.25 by Long Division Method
The long division method is particularly used for non-perfect square numbers and decimal numbers. In this method, we should check the grouping of digits 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, consider the number 10.25. Place a decimal point and pair the digits before and after the decimal point.
Step 2: Find the largest number whose square is less than or equal to 10. We can choose 3 because 3 × 3 = 9. Subtract 9 from 10, and bring down the next pair of digits, 25, making the new dividend 125.
Step 3: Double the current quotient (3), giving us 6, which will be our new divisor base.
Step 4: Find a digit x such that 6x × x is less than or equal to 125. The suitable digit is 2, making the divisor 62 and the product 62 × 2 = 124.
Step 5: Subtract 124 from 125, leaving a remainder of 1.
Since there are no more pairs of digits, the quotient, 3.2, is the square root of 10.25.
Square Root of 10.25 by Approximation Method
Approximation method is another method for finding square roots; it is an easy method to approximate the square root of a given number. Now let us learn how to find the square root of 10.25 using the approximation method:
Step 1: Identify the perfect squares around 10.25. The closest perfect square less than 10.25 is 9, and the closest perfect square greater than 10.25 is 16.
Step 2: Knowing that √9 = 3 and √16 = 4, we can see that √10.25 is between 3 and 4.
Step 3: Narrow down by approximation. Since 10.25 is closer to 9, we try 3.2. Calculate 3.2 × 3.2 = 10.24, which is very close.
Thus, the square root of 10.25 is approximately 3.2.
Common Mistakes and How to Avoid Them in the Square Root of 10.25
Students often make mistakes while finding square roots, such as misunderstanding the concept of perfect squares and applying incorrect methods. Let us look at a few common mistakes students tend to make and how to avoid them in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots. However, we typically use only the positive square root, as it is the required one for most applications.
For example, √10.25 = ±3.2, but we often use 3.2 in practical scenarios.
Square Root of 10.25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √10.25?
The area of the square is 10.25 square units.
Explanation
The area of a square is side².
The side length is given as √10.25.
Area of the square = side² = √10.25 × √10.25 = 3.2 × 3.2 = 10.25.
Therefore, the area of the square box is 10.25 square units.
Problem 2
A square-shaped garden measuring 10.25 square feet is built; if each of the sides is √10.25, what will be the square feet of half of the garden?
5.125 square feet
Explanation
We can determine half of the garden's area by dividing the given area by 2, as the garden is square-shaped.
Dividing 10.25 by 2, we get 5.125.
So, half of the garden measures 5.125 square feet.
Problem 3
Calculate √10.25 × 5.
16
Explanation
The first step is to find the square root of 10.25, which is 3.2.
The second step is to multiply 3.2 by 5.
So, 3.2 × 5 = 16.
Problem 4
What will be the square root of (6.25 + 4)?
The square root is 3.2.
Explanation
To find the square root, we need to find the sum of (6.25 + 4). 6.25 + 4 = 10.25, and then 10.25 = 3.2.
Therefore, the square root of (6.25 + 4) is ±3.2.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √10.25 units and the width ‘w’ is 5 units.
The perimeter of the rectangle is 16.4 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√10.25 + 5) = 2 × (3.2 + 5) = 2 × 8.2 = 16.4 units.
FAQ on Square Root of 10.25
1.What is √10.25 in its simplest form?
2.Can 10.25 be expressed as a fraction?
3.Calculate the square of 3.2.
4.Is 10.25 a rational number?
5.What is the principal square root of 10.25?
Important Glossaries for the Square Root of 10.25
- Square root: A square root of a number is a value that, when multiplied by itself, gives the original number. Example: 3.2² = 10.24, and the inverse of the square is the square root, so √10.25 = 3.2.
- Rational number: A rational number is a number that can be expressed 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 or a rational number. Example: 10.25 is a perfect square because √10.25 = 3.2.
- Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
- Long division method: A step-by-step process used to find the square root of a number, especially useful for numbers that are not perfect squares or for decimal numbers.
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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.
