123 LearnersLast updated on May 26th, 2025
Square Root of 10900
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 10900.
What is the Square Root of 10900?
The square root is the inverse of the square of a number. 10900 is not a perfect square. The square root of 10900 is expressed in both radical and exponential form. In the radical form, it is expressed as √10900, whereas (10900)^(1/2) in the exponential form. √10900 ≈ 104.403, 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 10900
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are generally used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 10900 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 10900 is broken down into its prime factors.
Step 1: Finding the prime factors of 10900
Breaking it down, we get 2 x 2 x 5 x 5 x 109: 2^2 x 5^2 x 109
Step 2: Now we have found the prime factors of 10900. The second step is to make pairs of those prime factors. Since 10900 is not a perfect square, it cannot be grouped into complete pairs. Therefore, calculating 10900 using prime factorization is not straightforward.
Square Root of 10900 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 10900, we need to group it as 00 and 109.
Step 2: Now we need to find n whose square is closest to 109. We can say n is '10' because 10^2 = 100 is less than or equal to 109. Now the quotient is 10, and after subtracting, the remainder is 9.
Step 3: Now let us bring down 00, making the new dividend 900. Add the old divisor with the same number 10 + 10, we get 20, which will be our new divisor.
Step 4: The new divisor will be the sum of the current divisor and the quotient. Now we get 20n as the new divisor, and we need to find the value of n.
Step 5: The next step is finding 20n × n ≤ 900. Let us consider n as 4, now 204 x 4 = 816.
Step 6: Subtracting 816 from 900 gives a difference of 84, and the quotient becomes 104.
Step 7: Since the dividend is less than the divisor, we need to add a decimal point, allowing us to add two zeroes to the dividend. Now the new dividend is 8400.
Step 8: Now we need to find the new divisor, which is 208, as 2084 × 4 = 8336.
Step 9: Subtracting 8336 from 8400 gives a result of 64.
Step 10: Now the quotient is 104.4.
Step 11: Continue performing these steps until we get two numbers after the decimal point. If there is no decimal value, continue until the remainder is zero.
So the square root of √10900 is approximately 104.40.
Square Root of 10900 by Approximation Method
The approximation method is another method for finding square roots and is an easy way to estimate the square root of a given number. Now let us learn how to find the square root of 10900 using the approximation method.
Step 1: Now we have to find the closest perfect squares around √10900. The smallest perfect square less than 10900 is 10000 (100^2), and the largest perfect square more than 10900 is 11025 (105^2). √10900 falls somewhere between 104 and 105.
Step 2: Now we apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) So, (10900 - 10000) ÷ (11025 - 10000) = 900 ÷ 1025 ≈ 0.878
Using the formula, we identified the decimal part of our square root. The next step is adding the value we got initially to the decimal number, which is 104 + 0.878 ≈ 104.40. Thus, the square root of 10900 is approximately 104.40.
Common Mistakes and How to Avoid Them in the Square Root of 10900
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping steps in long division methods. 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 usually take only the positive square root, as it is the required one.
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 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 next step.
For example, √(12 + 24) = √12 + √24 is an incorrect method of using roots. The right way 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, resulting in a wrong answer at the end of the sum. This may either happen in subtracting or elsewhere.
Square Root of 10900 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √900?
The area of the square is 900 square units.
Explanation
The area of the square = side^2.
The side length is given as √900.
Area of the square = side^2 = √900 × √900 = 30 × 30 = 900.
Therefore, the area of the square box is 900 square units.
Problem 2
A square-shaped building measuring 10900 square feet is built; if each of the sides is √10900, what will be the square feet of half of the building?
5450 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 10900 by 2 = we get 5450.
So half of the building measures 5450 square feet.
Problem 3
Calculate √10900 × 5.
522.015
Explanation
The first step is to find the square root of 10900, which is approximately 104.403.
The second step is to multiply 104.403 by 5.
So 104.403 × 5 ≈ 522.015.
Problem 4
What will be the square root of (10000 + 900)?
The square root is approximately 104.40.
Explanation
To find the square root, we need to find the sum of (10000 + 900). 10000 + 900 = 10900, and then √10900 ≈ 104.40.
Therefore, the square root of (10000 + 900) is approximately ±104.40.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √900 units and the width ‘w’ is 100 units.
We find the perimeter of the rectangle as 260 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√900 + 100) = 2 × (30 + 100) = 2 × 130 = 260 units.
FAQ on Square Root of 10900
1.What is √10900 in its simplest form?
2.Mention the factors of 10900.
3.Calculate the square of 10900.
4.Is 10900 a prime number?
5.10900 is divisible by?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 10900?
8.How do technology and digital tools in India support learning Algebra and Square Root of 10900?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for the Square Root of 10900
- Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse operation is the square root, so √16 = 4.
- Irrational number: An irrational number is a number that cannot be written as a simple fraction p/q, where q is not equal to zero, and p and q are integers.
- Approximation method: A method used to find an approximate value of a non-perfect square root.
- Long division method: A method used to find the square root of a number by dividing it into smaller parts.
- Perfect square: A number that is the square of an integer. For example, 100 is a perfect square because 10 × 10 = 100.
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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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