131 LearnersLast updated on May 26th, 2025
Square Root of 10201
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 10201.
What is the Square Root of 10201?
The square root is the inverse of the square of the number. 10201 is a perfect square. The square root of 10201 is expressed in both radical and exponential form. In radical form, it is expressed as √10201, whereas (10201)^(1/2) in exponential form. √10201 = 101, 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 10201
The prime factorization method is used for perfect square numbers, such as 10201. For non-perfect square numbers, methods like long-division and approximation are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 10201 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 10201 is broken down into its prime factors.
Step 1: Finding the prime factors of 10201
Breaking it down, we get 101 x 101: 101^2
Step 2: Now we found out the prime factors of 10201. Since 10201 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating 10201 using prime factorization gives us √10201 = 101.
Square Root of 10201 by Long Division Method
The long division method is useful for both perfect and 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 10201, we need to group it as 01, 20, and 10.
Step 2: Now we need to find n whose square is less than or equal to 10. We can use n = 3 because 3 x 3 = 9, which is less than 10. The quotient is 3, and the remainder is 1.
Step 3: Bring down the next pair 20 to make it 120. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: The new divisor will be placed beside the dividend to make it 6n as the new divisor. We need to find the value of n.
Step 5: The next step is finding 6n x n ≤ 120; let us consider n as 2, so 62 x 2 = 124, which is too large. Try n = 1, so 61 x 1 = 61.
Step 6: Subtract 120 - 61, and the difference is 59, and the quotient is 31.
Step 7: Bring down the next pair 01 to make it 5901. Add the old divisor with the same number 61 + 1 to get 62, which will be our new divisor.
Step 8: The next step is finding 62n x n ≤ 5901; let us consider n as 9, so 629 x 9 = 5661.
Step 9: Subtract 5901 - 5661, and the difference is 240, and the quotient is 310.
Step 10: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 24000.
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 √10201 is 101.
Square Root of 10201 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 10201 using the approximation method.
Step 1: Now we have to find the closest perfect square of √10201. The closest perfect square of 10201 is 10000 and 10404. √10201 falls between 100 and 102.
Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (10201 - 10000) / (10404 - 10000) = 201 / 404 = 0.4975.
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 100 + 0.4975 ≈ 100.5, so the square root of 10201 is approximately 101, which we know is exact by other methods.
Common Mistakes and How to Avoid Them in the Square Root of 10201
Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping long division methods, etc. 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: √10201 = 101, there is also -101 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 before moving on to the second step.
For example: √(100 + 100) ≠ √100 + √100. The right way is √(100 + 100) = √200.
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 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. This may happen in subtracting or elsewhere.
Square Root of 10201 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √10201?
The area of the square is 10201 square units.
Explanation
The area of the square = side^2.
The side length is given as √10201.
Area of the square = side^2 = √10201 x √10201 = 101 x 101 = 10201.
Therefore, the area of the square box is 10201 square units.
Problem 2
A square-shaped building measuring 10201 square feet is built; if each of the sides is √10201, what will be the square feet of half of the building?
5100.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 10201 by 2 = we get 5100.5.
So half of the building measures 5100.5 square feet.
Problem 3
Calculate √10201 x 5.
505
Explanation
The first step is to find the square root of 10201, which is 101.
The second step is to multiply 101 with 5.
So 101 x 5 = 505.
Problem 4
What will be the square root of (9801 + 400)?
The square root is 101.
Explanation
To find the square root, we need to find the sum of (9801 + 400). 9801 + 400 = 10201, and then √10201 = 101.
Therefore, the square root of (9801 + 400) is ±101.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √10201 units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 278 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√10201 + 38) = 2 × (101 + 38) = 2 × 139 = 278 units.
FAQ on Square Root of 10201
1.What is √10201 in its simplest form?
2.Mention the factors of 10201.
3.Calculate the square of 10201.
4.Is 10201 a prime number?
5.10201 is divisible by?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 10201?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 10201?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for the Square Root of 10201
- Square root: A square root is the inverse of a square. Example: 10^2 = 100, and the inverse of the square is the square root that is √100 = 10.
- Perfect square: A perfect square is a number that has a whole number as its square root. For example, 16 is a perfect square because √16 = 4.
- 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.
- Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, 10201 = 101 x 101.
- Long division method: A method used to find the square root of numbers by dividing the number into groups and using division steps to reach the square root.
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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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