160 LearnersLast updated on May 26th, 2025
Square Root of 7921
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 7921.
What is the Square Root of 7921?
The square root is the inverse of the square of the number. 7921 is a perfect square. The square root of 7921 is expressed in both radical and exponential form. In radical form, it is expressed as √7921, whereas (7921)^(1/2) in exponential form. √7921 = 89, 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 7921
The prime factorization method is used for perfect square numbers. However, other methods like the long-division method and approximation method can also be used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 7921 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 7921 is broken down into its prime factors.
Step 1: Finding the prime factors of 7921 Breaking it down, we get 89 x 89: 89²
Step 2: Now we have found the prime factors of 7921. The second step is to make pairs of those prime factors. Since 7921 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating 7921 using prime factorization gives us √7921 = 89.
Square Root of 7921 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 7921, we group it as 79 and 21.
Step 2: Now we need to find n whose square is less than or equal to 79. We can say n as ‘8’ because 8 x 8 = 64 is less than 79. Now the quotient is 8, after subtracting 64 from 79 the remainder is 15.
Step 3: Let us bring down 21, making the new dividend 1521. Add the old divisor with the same number 8 + 8, we get 16 which will be our new divisor.
Step 4: The new divisor will be 16n. Now we need to find the value of n such that 16n x n ≤ 1521. Let us consider n as 9, now 169 x 9 = 1521.
Step 5: Subtract 1521 from 1521, the remainder is 0, and the quotient is 89. The square root of √7921 is 89.
Square Root of 7921 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. However, since 7921 is a perfect square, the approximation method is not necessary, as the exact answer is already known: √7921 = 89.
Common Mistakes and How to Avoid Them in the Square Root of 7921
Students do make mistakes while finding the square root, such as 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: √50 = 7.07, there is also -7.07 which should not be forgotten.
Square Root of 7921 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √7921?
The area of the square is 7921 square units.
Explanation
The area of the square = side². The side length is given as √7921. Area of the square = side² = √7921 x √7921 = 89 × 89 = 7921. Therefore, the area of the square box is 7921 square units.
Problem 2
A square-shaped building measuring 7921 square feet is built; if each of the sides is √7921, what will be the square feet of half of the building?
3960.5 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped. Dividing 7921 by 2, we get 3960.5. So half of the building measures 3960.5 square feet.
Problem 3
Calculate √7921 x 5.
445
Explanation
The first step is to find the square root of 7921, which is 89. The second step is to multiply 89 with 5. So 89 x 5 = 445.
Problem 4
What will be the square root of (13456 + 7921)?
The square root is 145
Explanation
To find the square root, we need to find the sum of (13456 + 7921). 13456 + 7921 = 21377, and then √21377 ≈ 145. Therefore, the square root of (13456 + 7921) is approximately ±145.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √7921 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is 254 units.
Explanation
Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√7921 + 38) = 2 × (89 + 38) = 2 × 127 = 254 units.
FAQ on Square Root of 7921
1.What is √7921 in its simplest form?
2.Mention the factors of 7921.
3.Calculate the square of 89.
4.Is 7921 a prime number?
5.7921 is divisible by?
Important Glossaries for the Square Root of 7921
- Square root: A square root is the inverse of squaring a number. Example: 8² = 64, and the inverse of squaring is the square root that is √64 = 8.
- 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, 89² = 7921.
- Long division method: A method used to find square roots of both perfect and non-perfect squares by dividing the number into groups.
- Approximation method: A method used to find an approximate value of the square root of a non-perfect square when the exact value is not necessary.
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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.
