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Last updated on May 26th, 2025

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Square root of 56

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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 56 for Filipino Students
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What Is the Square Root of 56?

The square root of 56 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y × y, the result is 56. It contains both positive and a negative root, where the positive root is called the principal square root. The square root of 56 is ±7.48331477355. The positive value, 7.48331477355 is the solution of the equation x2 = 56. As defined, the square root is just the inverse of squaring a number, so, squaring 7.48331477355 will result in 56.  The square root of 56 is expressed as √56 in radical form, where the ‘√’  sign is called “radical”  sign. In exponential form, it is written as (56)1/2  

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Finding the Square Root of 56

We can find the square root of 56 through various methods. They are:


i) Prime factorization method


ii) Long division method


iii) Approximation/Estimation method
 

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Square Root of 56 By Prime Factorization Method

The prime factorization of 56 involves breaking down a number into its factors. Divide 56 by prime numbers, and continue to divide the quotients until they can’t be separated anymore. After factorizing 56, 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 56 = 2 × 2  × 2  × 7 


for 56, only one pairs of factors 2 can be obtained, but a single 2 and 7 are remaining.


So, it can be expressed as  √56 = √(2 × 2  ×2 ×7) = 2√14


2√14 is the simplest radical form of √56.

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Square Root of 56 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 56:


Step 1: Write the number 56, 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 56. Here, it is
             7, Because 72=49< 56.
Step 3 : Now divide 56 by 7 (the number we got from Step 2) such that we get 7 as quotient and we get a remainder. Double the divisor 7, we get 14, and then the largest possible number A1=4 is chosen such that when 4 is written beside the new divisor, 14, a 3-digit number is formed →144, and multiplying 4 with 144 gives 576 which is less than 700.

Repeat the process until you reach the remainder of 0


We are left with the remainder, 496 (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 7.48….
 

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Square Root of 56 by Approximation 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 56. Here, it is 49 and 64.


Step 2: We know that, √49=±7 and √64=±8. This implies that √56 lies between 7 and 8.

 

Step 3: Now we need to check √56 is closer to 7 or 7.5. Since (7)2=49 and (7.5)2=56.25. Thus, √56 lies between 7 and 7.5.

Step 4: Again considering precisely, we see that  √56 lies close to (7.5)2=56.25. Find squares of (7.47)2=55.80 and (7.49)2= 56.10.

 

We can iterate the process and check between the squares of 7.475 and 7.489 and so on.


We observe that √56 = 7.483…

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Common Mistakes and How to Avoid Them in the Square Root of 56

When we find the square root of 56, 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

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Assuming √56 as a simple fraction
 

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√56=7.48… which is an irrational number. Hence, it cannot be expressed as a fraction
 

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Square Root of 56 Examples

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Problem 1

Simplify √56 + √56 + √56?

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√56 + √56 + √56

 

= √56⤬3 = 2√14⤬3

 

= 6√14

 

= 6√14


Answer : 6√14
 

Explanation

Simplified the expression and found out the simplest radical form of √56 that is 2√14, applied that and solved.

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Problem 2

What is √56 multiplied by 2√56 and then divided by (√56)²?

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(√56 ⤬ 2√56)/(√56)2

 

= (56⤬2)/56

 

= 2


Answer: 2 
 

Explanation

√56  multiplying with itself gives 56, and then again multiplied by 2 in the first step and then again divided by (√56)2=56 
 

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Problem 3

Find the value of (1/√56)⤬ (1/√56)?

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(1/√56)⤬ (1/√56)

 

= 1/ 56

 

= 0.018


Answer: 0.018 
 

Explanation

 (1/√56)⤬ (1/√56)

= 1/56 as same as √56⤬ √56 = 56
 

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Problem 4

If y=√56, find y²⤬y³

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firstly, y=√56 


Now, squaring y, we get,


y2= (√56)2=56


or, y2=56


Similarly,  y3=(√56)3=56√56


y2⤬y3= 56 ⤬ 56√56

 

= 3136√56

 

= 3136⤬ 2√14

 

= 6272√14


Answer :6272√14
 

Explanation

squaring “y” which is same as squaring the value of √56 resulted to 
56 and hence applied this fact to each problem here.
 

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Problem 5

Find √56 / √49

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√56/√49

 

= √(56/49)

 

= 7.48/7

 

= 1.0685…


Answer : 1.0685… 
 

Explanation

finding out the square root values of √56 and √49 and then dividing.

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FAQs on 56 Square Root

1.What are the factors of 56?

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2.What is the value of √55?

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3.Is 56 a perfect square or non-perfect square?

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4.Is the square root of 56 a rational or irrational number?

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5.Is 56 a perfect cube?

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

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7.How can cultural or local activities in Philippines support learning Algebra topics such as Square root of 56?

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8.How do technology and digital tools in Philippines support learning Algebra and Square root of 56?

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

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Important Glossaries for Square Root of 56

  • 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, 34 = 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


 

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About BrightChamps in Philippines

At BrightChamps, we believe algebra is more than symbols—it’s a gateway to countless opportunities! Our mission is to support children across the Philippines in mastering key math skills, focusing today on the Square root of 56 with an emphasis on understanding square roots—in a lively, fun, and easy-to-follow way. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, tracking basketball scores, or managing their allowance to buy the latest gadgets, mastering algebra builds their confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Since kids in the Philippines learn in different styles, we tailor our approach to each learner. From Manila’s busy streets to the beautiful islands of Palawan, BrightChamps brings math to life, making it exciting and relevant throughout the Philippines. Let’s make square roots a fun part of every child’s math journey!
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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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