154 LearnersLast updated on May 26th, 2025
Square Root of 961
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 961.
What is the Square Root of 961?
The square root is the inverse of the square of the number. 961 is a perfect square. The square root of 961 is expressed in both radical and exponential form. In the radical form, it is expressed as √961, whereas (961)(1/2) in the exponential form. √961 = 31, 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 961
The prime factorization method is used for perfect square numbers. Since 961 is a perfect square number, the prime factorization method is applicable. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 961 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 961 is broken down into its prime factors.
Step 1: Finding the prime factors of 961 Breaking it down, we get 31 x 31.
Step 2: Now we found out the prime factors of 961. Since 961 is a perfect square, the digits of the number can be grouped in pairs.
Therefore, the square root of 961 using prime factorization is possible and is equal to 31.
Square Root of 961 by Long Division Method
The long division method is particularly used for both perfect and non-perfect square numbers. 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 961, we need to group it as 61 and 9.
Step 2: Now we need to find a number n whose square is less than or equal to 9. We can say n is '3' because 3 x 3 = 9. Now the quotient is 3.
Step 3: Now let us bring down 61, which is the new dividend. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.
Step 4: Multiply the new divisor 6 by n to find the value of n.
Step 5: The next step is finding 6n x n ≤ 61. Let us consider n as 1, now 6 x 1 x 1 = 61.
Step 6: Subtract 61 from 61, the remainder is 0.
So the square root of √961 is 31.
Square Root of 961 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 961 using the approximation method.
Step 1: Now we have to find the closest perfect squares of √961. The closest perfect squares are 900 and 1024. √961 falls exactly at 31.
Step 2: Since 961 is a perfect square, the square root is exactly 31 without the need for further approximation.
Common Mistakes and How to Avoid Them in the Square Root of 961
Students do make mistakes while finding the square root, such as forgetting about the negative square root or misapplying 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 will be taking only the positive square root, as it is the required one. For example: √961 = 31, there is also -31 which should not be forgotten.
Square root of 961 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √961?
The area of the square is 961 square units.
Explanation
The area of the square = side².
The side length is given as √961.
Area of the square = side² = √961 x √961 = 31 x 31 = 961
Therefore, the area of the square box is 961 square units.
Problem 2
A square-shaped building measuring 961 square feet is built; if each of the sides is √961, what will be the square feet of half of the building?
480.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 961 by 2, we get 480.5.
So half of the building measures 480.5 square feet.
Problem 3
Calculate √961 x 5.
155
Explanation
The first step is to find the square root of 961, which is 31.
The second step is to multiply 31 with 5.
So 31 x 5 = 155.
Problem 4
What will be the square root of (961 + 39)?
The square root is 32
Explanation
To find the square root,
we need to find the sum of (961 + 39) 961 + 39 = 1000, and then √1000 ≈ 31.62.
Therefore, the square root of (961 + 39) is approximately 31.62.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √961 units and the width ‘w’ is 39 units.
We find the perimeter of the rectangle as 140 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√961 + 39)
= 2 × (31 + 39) = 2 × 70 = 140 units.
FAQ on Square Root of 961
1.What is √961 in its simplest form?
2.Mention the factors of 961.
3.Calculate the square of 961.
4.Is 961 a prime number?
5.961 is divisible by?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 961?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 961?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for the Square Root of 961
- Square root: A square root is the inverse of a square. Example: 5² = 25 and the inverse of the square is the square root, that is √25 = 5.
- 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, 961 is a perfect square.
- Prime number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
- Long division method: A method used to find the square root of both perfect and non-perfect squares by dividing and approximating.
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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
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