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Last updated on May 26th, 2025

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Square root of 29

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The square root of 29 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 29. It contains both positive and a negative root, where the positive root is called the principal square root.

Square root of 29 for Vietnamese Students
Professor Greenline from BrightChamps

What Is the Square Root of 29?

The square root of 29 is ±5.38516480713.The positive value, 5.38516480713 is the solution of the equation x2 = 29. As defined, the square root is just the inverse of squaring a number, so, squaring 5.38516480713 will result in 29.  The square root of 29 is expressed as √29 in radical form, where the ‘√’  sign is called “radical”  sign. In exponential form, it is written as (29)1/2   

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Finding the Square Root of 29

We can find the square root of 29 through various methods. They are:

 

  • Prime factorization method

 

  • Long division method

 

  • Approximation/Estimation method
     
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Square Root of 29 By Prime Factorization Method


The prime factorization of 29 involves breaking down a number into its factors. Divide 29 by prime numbers, and continue to divide the quotients until they can’t be separated anymore. After factorizing 29, 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 29 = 29 × 1  

 
for 29, no pairs of factors are obtained, but a single 29 is obtained.


So, it can be expressed as  √29 = √(29 × 1) = √29


√29 is the simplest radical form of √29

 

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Square Root of 29 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 29:

 


Step 1 : Write the number 29, 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 29. Here, it is 5, Because 52=25 < 29

 

 

Step 3 : Now divide 29 by 5 (the number we got from Step 2) such that we get 5 as quotient, and we get a remainder. Double the divisor 5, we get 10 and then the largest possible number A1=3 is chosen such that when 3 is written beside the new divisor, 10, a 3-digit number is formed →103 and multiplying 3 with 103 gives 309 which is less than 400.

 

Repeat the process until you reach remainder 0

 


We are left with the remainder, 1775 (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, is 5385…

 

 

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Square Root of 29 by Approximation Method

Approximation or estimation of square root is not the exact square root, but it is an estimate.Here, through this method, an approximate value of square root is found by guessing.

 

Follow the steps below:


Step 1 : Identify the square roots of the perfect squares above and below 26


Below : 25→ square root of 25 = 5     ……..(i)


 Above : 36 →square root of 36= 6     ……..(ii)


Step 2 : Divide 29 with one of 5 or 6.


 If we choose 6, and divide 29 by 6, we get 4.833   …….(iii)


             
Step 3: Find the average of 6 (from (ii)) and 4.833 (from (iii))


(6+4.833)/2 = 5.4

           
 Hence, 5.4 is the approximate square root of 29
 

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Common Mistakes and How to Avoid Them in the Square Root of 29

When we find the square root of 26, 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

Incorrectly applying the square root property
 

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Square root do not distribute over additions. For example, √29 ≠  √19 +  √10
 

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Square Root of 29 Examples

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Problem 1

Simplify 15√29 (15√29+15√29)?

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15√29 (15√29+15√29)

 

= 15√29(15√29⤬2)

 

=15√29(15⤬5.385⤬2)

 

=15√29(161.55)

 

= 15⤬5.385⤬161.55

 

= 13049.2012


Answer : 13049.2012
 

Explanation

 √29= 5.385, so multiplying the square root value with 15 in each part and then simplifying
 

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Problem 2

What is (√29 +√30+√31) ?

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29 +√30+√31

 

= 5.385 + 5.477 + 5.567

 

= 16.429


Answer: 16.429
 

Explanation

 adding the square root value of 29, square root value of 30 and square root value of 31 

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Problem 3

Find :(√29 ⤬√29)/(√10⤬ √10)

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 (√29 ⤬√29)/(√10⤬ √10)

 

= 29/10

 

=2.9


Answer: 2.9
 

Explanation

√29 ⤬√29 =29 and √10⤬ √10 =10. Using these, we divided the values
 

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Problem 4

Find the difference between (√26)^2 - (√25)^2+ (√26)^2

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(√26)2 - (√25)2+ (√26)2


= 26 -25+26


=27


Answer: 27
 

Explanation

find out the square values of √26 and √25 and then simplified
 

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Problem 5

Find (√29 / √16)⤬√29

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 (√29/√16)⤬√29

 

= √(29⤬29)/√16

 

= 29/4

 

= 7.25


Answer : 7.25
 

Explanation

Since, √29⤬√29=29 so we simplified and divide by the √16 which is equal to 4 
 

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FAQs on 29 Square Root

1.How to solve √28?

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2.What is the cube root of 29 ?

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3.Is 29 a perfect square or non-perfect square?

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4.Is the square root of 29 a rational or irrational number?

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5.Is 28 a perfect square?

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

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7.How can cultural or local activities in Vietnam support learning Algebra topics such as Square root of 29?

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8.How do technology and digital tools in Vietnam support learning Algebra and Square root of 29?

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

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Professor Greenline from BrightChamps

Important Glossaries for Square Root of 29

  • 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: 2 × 2 × 2 × 2 = 16 Or, 24 = 16, where 2 is the base, 4 is the exponent 

 

  • Prime Factorization:  Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3

 

  • 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 :3, 8, 24
Professor Greenline from BrightChamps

About BrightChamps in Vietnam

At BrightChamps, we know algebra is more than symbols—it’s a path to countless opportunities! Our goal is to help children across Vietnam grasp essential math skills, with today’s focus on the Square root of 29 and a special look at square roots—in an engaging, enjoyable, and easy-to-learn way. Whether your child is figuring out how fast a roller coaster moves at Suoi Tien Theme Park, keeping track of local football scores, or budgeting their allowance for new gadgets, mastering algebra gives them the confidence to handle daily challenges. Our interactive lessons make learning easy and fun. Since children in Vietnam learn in different ways, we adapt to each learner’s style. From Ho Chi Minh City’s vibrant streets to the beautiful Ha Long Bay, BrightChamps makes math come alive throughout Vietnam. Let’s make square roots an exciting part of every child’s math adventure!
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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.

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Fun Fact

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

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