122 LearnersLast updated on May 26th, 2025
Square Root of 981
If a number is multiplied by the same number, the result is a square. The inverse of squaring is finding the square root. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 981.
What is the Square Root of 981?
The square root is the inverse operation of squaring a number. 981 is not a perfect square. The square root of 981 can be expressed in both radical and exponential form. In radical form, it is expressed as √981, whereas in exponential form as (981)(1/2). √981 ≈ 31.32092, which is an irrational number because it cannot be expressed as a fraction of two integers where the denominator is not zero.
Finding the Square Root of 981
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, we use methods like the long division method and the approximation method. Let us explore these methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 981 by Prime Factorization Method
Prime factorization involves expressing a number as the product of its prime factors. Let us break down 981 into its prime factors:
Step 1: Finding the prime factors of 981 Breaking it down, we get 3 x 3 x 109: 3^2 x 109^1
Step 2: Now that we have found the prime factors of 981, we attempt to form pairs of prime factors. Since 981 is not a perfect square, the digits of the number cannot be grouped into pairs, making it impossible to calculate √981 using prime factorization directly.
Square Root of 981 by Long Division Method
The long division method is particularly useful for non-perfect square numbers. This method involves finding a series of approximations to reach the square root. Here is how you can find the square root using the long division method, step by step:
Step 1: Group the digits of the number in pairs from right to left. For 981, we group it as 9 and 81.
Step 2: Find n such that n2 is less than or equal to 9. Here, n is 3 because 3 x 3 = 9. Subtract 9 from 9, and the remainder is 0.
Step 3: Bring down the next pair of digits, 81, making the new dividend 81. Double the quotient obtained in the previous step (3), giving a new divisor of 6.
Step 4: Find a digit x such that 6x multiplied by x is less than or equal to 81. Here x is 1 because 61 x 1 = 61. Subtract 61 from 81 to get a remainder of 20.
Step 5: Bring down two zeros to make the dividend 2000. Double the quotient (31), making the new divisor 62.
Step 6: Find a digit y such that 62y x y is less than or equal to 2000. Here y is 3 because 623 x 3 = 1869. Subtract 1869 from 2000 to get a remainder of 131.
Step 7: Repeat the process to obtain more decimal places.
The quotient so far is 31.32. So the square root of √981 is approximately 31.32.
Square Root of 981 by Approximation Method
The approximation method is an easy way to estimate the square roots of numbers. Here's how to approximate the square root of 981:
Step 1: Find the closest perfect squares around 981. The closest perfect squares are 961 (312) and 1024 (322). √981 falls between 31 and 32.
Step 2: Apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). (981 - 961) / (1024 - 961) = 20 / 63 ≈ 0.317
Using the formula, the approximate decimal part is 0.317. Adding this to the integer part gives us 31 + 0.317 ≈ 31.317.
Thus, the square root of 981 is approximately 31.317.
Common Mistakes and How to Avoid Them in the Square Root of 981
Students often make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at some common mistakes in detail.
Mistake 1
Forgetting about the negative square root
It is important to remember that every positive number has both a positive and a negative square root. However, we typically only use the positive square root in most practical applications. For example, √81 = 9, but there is also -9.
Square Root of 981 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √981?
The area of the square is approximately 981 square units.
Explanation
The area of a square is given by side2.
If the side length is √981, then the area is (√981)² = 981.
Therefore, the area of the square box is approximately 981 square units.
Problem 2
A square-shaped garden measuring 981 square feet is built; if each side is √981, what will be the area of half of the garden?
490.5 square feet
Explanation
Since the garden is square-shaped, its area is evenly divided.
Dividing 981 by 2 gives 490.5,
so half of the garden measures 490.5 square feet.
Problem 3
Calculate √981 x 5.
Approximately 156.6
Explanation
First, find the square root of 981, which is approximately 31.32.
Then multiply 31.32 by 5 to get approximately 156.6.
Problem 4
What will be the square root of (961 + 20)?
The square root is approximately 31.32
Explanation
First, find the sum of 961 + 20, which is 981
. Then find the square root of 981, which is approximately 31.32.
Therefore, the square root of (961 + 20) is approximately 31.32.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √981 units and the width ‘w’ is 40 units.
The perimeter of the rectangle is approximately 142.64 units.
Explanation
Perimeter of a rectangle = 2 × (length + width)
Perimeter = 2 × (√981 + 40)
= 2 × (31.32 + 40) ≈ 2 × 71.32 ≈ 142.64 units.
FAQ on Square Root of 981
1.What is √981 in its simplest form?
2.What are the factors of 981?
3.Calculate the square of 981.
4.Is 981 a prime number?
5.What numbers is 981 divisible by?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 981?
8.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 981?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for the Square Root of 981
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: 42 = 16, so the square root of 16 is √16 = 4.
- Irrational number: A number that cannot be expressed as a simple fraction, with a non-repeating, non-terminating decimal expansion.
- Long division method: A step-by-step process used to find the square root of a non-perfect square by dividing and averaging.
- Approximation: An approach to estimating a number or value, often used when an exact calculation is not possible or necessary.
- Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 42.
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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.
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