309 LearnersLast updated on May 26th, 2025
Square root of 91.
When someone asks you to explain a square root, you can just tell that it is a number when multiplied by itself produces the same number. As we continue with our explanation, let’s assume the value of 91 Here 91 is considered as a non-perfect square root since it contain either decimal or fraction. Let's learn more about square roots in this article.
What is the square root of 91?
The square root of 91 can be easily found out by using long division method. In which it is discovered that the cumulative approximation of √91 is 9.539.
Finding the square root of 91.
There are many ways through which students can find square roots, and some of these methods are very popular. Some of the methods have been explained in detail below.
Square root of 91 using the prime factorization method.
In this method, we decompose the number into its prime factors.
Prime factorization of 91: 91=7×13.
Since not all prime factors can be paired, 91 cannot be simplified into a perfect square. Therefore, the square root of 91 cannot be expressed in a simple radical form.
Square root of 91 using the division method.
For non-perfect squares, we often use the nearest perfect square to estimate the square root. Follow these steps:
Step 1: Write the number 91 to perform long division.
Step 2: Identify a perfect square number that is less than or equal to 91. For 91, that number is 81 (92).
Step 3: Divide 91 by 9. The remainder will be 10, and the quotient will be 9.
Step 4: Bring down the remainder (10) and append two zeros. Add a decimal point to the quotient, making it 9.0.
Step 5: Double the quotient to use as the new divisor, which gives 18.
Step 6: Select a number that, when multiplied by the new divisor, results in a product less than or equal to 1800.
Step 7: Continue the division process to find √91 to the desired decimal places. → √91 ≈ 9.539.
Square root of 91 using the approximation method
In the approximation method, we estimate the square root by identifying the closest perfect squares surrounding the number.
Step 1: The nearest perfect squares to 91 are √100 = 10 and √81 = 9.
Step 2: Since 91 is between 100 and 81, we know the square root will be between 10 and 9.
Step 3: By testing numbers like 9.5, 9.6, and further, we find that √91 ≈ 9.539.
Common mistakes when finding the square root of 91.
Here are some common mistakes students should avoid while learning to calculate the square root of 91.
Mistake 1
Confusing Square Roots with Cubes
It's a pretty common mistake where students get confused between square and cube root, one must remember that square root is represented as (√) and cube root is represented as (∛).
Mistake 2
Getting confused between square of a number and square root
Students should remember that square of a number and square root are two opposite operations, For example, 76² is 5776, while √76 ≈ 8.717798.
Mistake 3
Not simplifying completely
Sometimes students forget to simplify the number completely, for example, √48 can be simplified to √(16 × 3) = 4√3. Always look for pairs of factors to simplify.
Square root of 91 Example
Problem 1
Find out if 64 is a perfect square.
→ √64
= 8
Explanation
64 is indeed a perfect square, as it is the result of multiplication between 8 and 8 itself.
Problem 2
How do you find the square root of a non-perfect square, such as √20.
→ √20
√20 = 2√5
Explanation
20 can be factored as 5 × 4 and 4 can be further factorized to 2 hence the final answer would be 2√5.
Problem 3
Simplify 6√18 – 2√18.
→ Factor √18
6√18 – 2√18
= √18(6-2)
= 4×4.243
= 16.972
Explanation
Simplification of √18= 4.243, now if you subtract the 2 from 6 and multiply it by 4.243 we get 16.972.
FAQs on the square root of 91.
1.What is cube root?
2. How do you simplify 5√72?
3. Name all the divisors of 91.
4.7 is the square root of what number?
5.Is 91 a prime number?
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 91.?
8.How do technology and digital tools in United States support learning Algebra and Square root of 91.?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square Root of 91.
- Square Root: A number which when is multiplied by itself gives the original number is called a square root.
- Perfect Square: A number that is the integral square of an integer I such that n = I², example I = 1, 2, 3, n = 1, 4, 9, 16, etc.
- Prime Factorization: The ability to factorize a number in to the product of the basic arithmetic numbers, also known as primary numbers.
- Non-Perfect Square: A figure that cannot be converted into an integer figure once divided by itself (e.g., 76).
- Approximation Method: Approximating square root, that is, finding the closest integer which, when squared, yields the number being approximated.
Explore More algebra
About BrightChamps in United States
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.
