BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon104 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of 991

Professor Greenline Explaining Math Concepts

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 various fields such as engineering, architecture, and finance. Here, we will discuss the square root of 991.

Square Root of 991 for Qatari Students
Professor Greenline from BrightChamps

What is the Square Root of 991?

The square root is the inverse of the square of the number. 991 is not a perfect square. The square root of 991 is expressed in both radical and exponential form. In the radical form, it is expressed as √991, whereas \(991^{1/2}\) in the exponential form. √991 ≈ 31.496, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 991

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers like 991, the long-division method and approximation method are used. Let us now learn the following methods: - Prime factorization method - Long division method - Approximation method

Professor Greenline from BrightChamps

Square Root of 991 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 991 is broken down into its prime factors. Step 1: Finding the prime factors of 991 991 is a prime number and cannot be broken down into smaller factors. Therefore, calculating √991 using prime factorization is not possible.

Professor Greenline from BrightChamps

Square Root of 991 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we find the square root step by step: Step 1: To begin with, we need to group the numbers from right to left. In the case of 991, we need to group it as 91 and 9. Step 2: Now we need to find n whose square is less than or equal to 9. We can choose n as '3' because \(3 \times 3 = 9\), which is equal to 9. Now the quotient is 3 after subtracting 9 from 9, leaving the remainder as 0. Step 3: Now let us bring down 91 which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6 which will be our new divisor. Step 4: The new divisor will be 6n. We need to find the value of n such that \(6n \times n \leq 91\). Let us consider n as 1, now \(61 \times 1 = 61\). Step 5: Subtract 91 from 61, the difference is 30, and the quotient becomes 31. Step 6: 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 3000. Step 7: Now we need to find the new divisor which is 631, because \(631 \times 4 = 2524\). Step 8: Subtracting 2524 from 3000, we get the result 476. Step 9: The quotient is 31.4. Continue these steps until we get the desired decimal precision. So the square root of √991 ≈ 31.496.

Professor Greenline from BrightChamps

Square Root of 991 by Approximation Method

The approximation method is another method for finding square roots, and 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 991 using the approximation method. Step 1: Now we have to find the closest perfect squares to √991. The smallest perfect square less than 991 is 961 (31^2) and the largest perfect square greater than 991 is 1024 (32^2). √991 falls somewhere between 31 and 32. 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: (991 - 961) / (1024 - 961) = 30/63 ≈ 0.476 Using the formula, we identified that the decimal point of our square root is approximately 0.476. The next step is adding the value we got initially to the decimal number, which is 31 + 0.476 ≈ 31.476. Therefore, the square root of 991 is approximately 31.476.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 991

Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping steps in the long division method. Now let us look at a few common mistakes in detail.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting about the negative square root

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

It is important to make students aware that a number has both positive and negative square roots. However, we take only the positive square root as it is typically the required one. For example: √50 = 7.071, but there is also -7.071 which should not be forgotten.

Max from BrightChamps Saying "Hey"

Square Root of 991 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √991?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The area of the square is approximately 982 square units.

Explanation

The area of the square = side². The side length is given as √991. Area of the square = side² = (√991)² = 991. Therefore, the area of the square box is 991 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 991 square feet is built; if each of the sides is √991, what will be the square feet of half of the building?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

495.5 square feet

Explanation

Divide the given area by 2 as the building is square-shaped. Dividing 991 by 2 = 495.5. So half of the building measures 495.5 square feet.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √991 × 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Approximately 157.48

Explanation

First, find the square root of 991, which is approximately 31.496. Then multiply 31.496 by 5. So, 31.496 × 5 ≈ 157.48.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (991 + 9)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The square root is approximately 32.

Explanation

First, find the sum of (991 + 9) = 1000, and then find the square root of 1000, which is approximately 31.62. Therefore, the square root of (991 + 9) is approximately 31.62.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √991 units and the width ‘w’ is 50 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The perimeter of the rectangle is approximately 162.99 units.

Explanation

Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√991 + 50) ≈ 2 × (31.496 + 50) ≈ 2 × 81.496 ≈ 162.99 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 991

1.What is √991 in its simplest form?

Math FAQ Answers Dropdown Arrow

2.Mention the factors of 991.

Math FAQ Answers Dropdown Arrow

3.Calculate the square of 991.

Math FAQ Answers Dropdown Arrow

4.Is 991 a prime number?

Math FAQ Answers Dropdown Arrow

5.991 is divisible by?

Math FAQ Answers Dropdown Arrow

6.How does learning Algebra help students in Qatar make better decisions in daily life?

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 991?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 991?

Math FAQ Answers Dropdown Arrow

9.Does learning Algebra support future career opportunities for students in Qatar?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 991

Square Root: A square root is the inverse of a square. For example, \(4^2 = 16\) and the inverse of the square is the square root, so \(√16 = 4\). Irrational Number: An irrational number is a number that cannot be written in the form of \(\frac{p}{q}\), where q is not equal to zero and p and q are integers. Long Division Method: A method used for calculating the square roots of non-perfect squares by dividing step by step. Perfect Square: A number that is the square of an integer. For example, 16 is a perfect square because \(4^2 = 16\). Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 991 is a prime number.

Professor Greenline from BrightChamps

About BrightChamps in Qatar

At BrightChamps, we know algebra is more than just symbols—it opens doors to many possibilities! Our aim is to support children all over Qatar in mastering key math skills, focusing today on the Square Root of 991 with a special focus on square roots—in a lively, engaging, and easy-to-understand way. Whether your child is calculating the speed of a roller coaster at Qatar’s Angry Birds World, tracking scores at local football matches, or managing their allowance for the latest gadgets, mastering algebra builds their confidence to face everyday challenges. Our interactive lessons make learning both fun and simple. Since kids in Qatar learn in various ways, we tailor our approach to each learner. From Doha’s modern cityscape to desert landscapes, BrightChamps makes math relatable and exciting throughout Qatar. Let’s make square roots a fun part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom