BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon284 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square root of 40

Professor Greenline Explaining Math Concepts

Square root is one of the most interesting mathematical topics to study. In daily life, square root functions are used in the field of engineering, GPS or distance calculations. Children use different approaches to solve square root problems. In this article, properties of square roots will be discussed.

Square root of 40 for Saudi Students
Professor Greenline from BrightChamps

What Is the Square Root of 40?

The square root of 40 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y × y, the result is 40. It contains both positive and a negative root, where the positive root is called the principal square root. The square root of 40 is ±6.32455532034. The positive value, 6.32455532034 is the solution of the equation x2 = 40.

As defined, the square root is just the inverse of squaring a number, so, squaring 6.32455532034 will result in 40.

The square root of 40 is expressed as √40 in radical form, where the ‘√’  sign is called the “radical”  sign. In exponential form, it is written as (40)1/2  
 

Professor Greenline from BrightChamps

Finding the Square Root of 40

We can find the square root of 40 through various methods. They are:


i) Prime factorization method


ii) Long division method


iii) Approximation/Estimation method
 

Professor Greenline from BrightChamps

Square Root of 40 By Prime Factorization Method

The prime factorization of 40 involves breaking down a number into its factors. Divide 40 by prime numbers, and continue to divide the quotients until they can’t be separated anymore. After factoring 40, make pairs out of the factors to get the square root.

 

If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

 

So, Prime factorization of 40 = 2 × 2  × 2  × 5 


for 40, only one pair of factors 2 can be obtained, but a single 2 and 5 are remaining.


So, it can be expressed as  √40 = √(2 × 2  ×2 ×5) = 2√10


2√10 is the simplest radical form of √40.
 

Professor Greenline from BrightChamps

Square Root of 40 by Long Division Method

This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 40:


Step 1: Write the number 40, and draw a bar above the pair of digits from right to left.
               
Step 2: Now, find the greatest number whose square is less than or equal to 40. Here, it is
             6, Because 62=36< 40.


Step 3 : Now divide 40 by 6 (the number we got from Step 2) such that we get 6 as quotient and we get a remainder. Double the divisor 6, we get 12, and then the largest possible number A1=3 is chosen such that when 3 is written beside the new divisor, 12, a 3-digit number is formed →123, and multiplying 3 with 123 gives 369 which is less than 400.

Repeat the process until you reach the remainder of 0


 We are left with the remainder, 7024 (refer to the picture), after some iterations and keeping the division till here, at this point 
             
Step 4 : The quotient obtained is the square root. In this case, it is 6.324….


 

Professor Greenline from BrightChamps

Square Root of 40 by Estimation Method

Estimation of square root is not the exact square root, but it is an estimate, or you can consider it as a guess.


Follow the steps below:


Step 1: Find the nearest perfect square number to 40. Here, it is 36 and 49.


Step 2: We know that, √36=±6 and √49=±7. This implies that √40 lies between 6 and 7.

 

Step 3: Now we need to check √40 is closer to 6 or 6.5. Since (6)2=36 and (6.5)2=42.25. Thus, √40 lies between 6 and 6.5.

 

Step 4: Again considering precisely, we see that  √40 lies close to (6.5)2=42.25. Find squares of (6.2)2=38.44 and (6.4)2= 40.96.

 

We can iterate the process and check between the squares of 6.3 and 6.39 and so on.


We observe that √40 = 6.324…
 

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 40

When we find the square root of 40, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.


 

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Assuming √40 as a simple fraction

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

√40=6.324… which is an irrational number. Hence, it cannot be expressed as a fraction
 

Max from BrightChamps Saying "Hey"

Square Root of 40 Examples

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

Problem 1

Simplify √40 + 5√40 + √40?

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

√40 + 5√40 + √40

 

= √40(1+5+1)

 

= 7√40 = 7⤬2√10

 

= 14√10

Explanation

 Simplified the expression and found out the simplest radical form of √40 that is 2√10, applied that and solved.

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

Problem 2

What is √40 multiplied by 2√40 and then divided by (√40)²?

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

 (√40 ⤬ 2√40)/(√40)2

 

= (40⤬2)/40

 

= 2


Answer: 2 
 

Explanation

√40  multiplying with itself gives 40, and then again multiplied by 2 in the first step and then again divided by (√40)2=40 
 

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

Problem 3

Find the value of (1/√40)⤬ (1/√40)?

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

 (1/√40)⤬ (1/√40) = 1/ 40 = 0.025 


Answer: 0.025

Explanation

(1/√40)⤬ (1/√40) = 1/ 40 as same as √40⤬ √40 =40
 

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

Problem 4

If y=√40, find y², y³

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

firstly, y=√40


Now, squaring y, we get,


y2= (√40)2=40


 or, y2=40


Similarly,  y3=(√40)3=40√40


Answer : 40,40√40
 

Explanation

squaring “y” which is same as squaring the value of √40 resulted to 40 and hence applied this fact to each problem here.
 

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

Problem 5

Find √40 / √49

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

√40/√49

 

= √(40/49)

 

= 5.477/7

 

= 0.782…

 


Answer : 0.782… 
 

Explanation

finding out the square root values of √40 and √49 and then dividing.
 

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

FAQs on 40 Square Root

1.How can you express √40 in fractional form ?

Math FAQ Answers Dropdown Arrow

2.What is the value of √42?

Math FAQ Answers Dropdown Arrow

3.Is 40 a perfect square or non-perfect square?

Math FAQ Answers Dropdown Arrow

4.Is the square root of 40 a rational or irrational number?

Math FAQ Answers Dropdown Arrow

5.How to solve √37?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square root of 40?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square root of 40?

Math FAQ Answers Dropdown Arrow

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

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for Square Root of 40

  • Exponential form - An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 3 ⤬ 3 ⤬ 3 ⤬ 3 = 81 Or, 3 4 = 81, where 3 is the base, 4 is the exponent 

 

  • Factorization - Expressing the given expression as a product of its factors Ex: 52=2 ⤬ 2 ⤬ 13 

 

  • Prime Numbers - Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

 

  • Rational numbers and Irrational numbers - The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

 

  • Perfect and non-perfect square numbers - Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :2, 8, 18


 
 

Professor Greenline from BrightChamps

About BrightChamps in Saudi Arabia

At BrightChamps, we recognize algebra as more than just symbols—it’s a key to unlock countless opportunities! Our goal is to help children across Saudi Arabia gain important math skills, focusing today on the Square root of 40 with special attention to square roots—in a way that’s engaging, lively, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Riyadh’s Al Hokair Land, following scores at local football matches, or managing their allowance for the latest gadgets, mastering algebra boosts their confidence for daily challenges. Our interactive lessons make learning accessible and fun. Since children in Saudi Arabia learn in different ways, we tailor lessons to suit each learner. From Riyadh’s bustling streets to Jeddah’s historic landmarks, BrightChamps brings math to life, making it exciting and relevant all over Saudi Arabia. Let’s make square roots a fun part of every child’s math adventure!
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