Square root of 14
2026-02-28 10:51 Diff
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Last updated on August 5, 2025

The square root of 14 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 14. It contains both positive and a negative root, where the positive root is called the principal square root.

What Is the Square Root of 14?

The square root of 14 is ±3.74165738677.The positive value,3.74165738677 is the solution of the equation x2 = 14. As defined, the square root is just the inverse of squaring a number, so, squaring 3.74165738677 will result in 14.  The square root of 14 is expressed as √14 in radical form, where the ‘√’  sign is called “radical”  sign. In exponential form, it is written as (14)1/2  
 

Finding the Square Root of 14

We can find the square root of 14 through various methods. They are:

  • Prime factorization method
  • Approximation/Estimation method
     

Square Root of 14 By Prime Factorization Method

The prime factorization of 14 involves breaking down a number into its factors. Divide 14 by prime numbers, and continue to divide the quotients until they can’t be separated anymore. After factorizing 14, 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 14 =2 × 7    


for 14, no pairs of factors are obtained, but a single 2 and a single 7 are obtained.


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


√14 is the simplest radical form of √14
 

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Square Root of 14 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 14:


Step 1 : Write the number 14, 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 14. Here, it is 3, Because 32=9 < 14

Step 3 : Now divide 14 by 3 (the number we got from Step 2) such that we get 3 as quotient, and we get a remainder. Double the divisor 3, we get 6 and then the largest possible number A1=7 is chosen such that when 7 is written beside the new divisor, 6, a 2-digit number is formed →67 and multiplying 7 with 67 gives 469 which is less than 500.

Repeat the process until you reach remainder 0


We are left with the remainder, 4919 (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 3.741…

Square Root of 14 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 14


Below : 9→ square root of 9 = 3     ……..(i)


 Above : 16 →square root of 16= 4     ……..(ii)


Step 2 : Divide 14 with one of 3 or 4


 If we choose 3, and divide 14 by 3, we get 4.666   …….(iii)

              Step 3: Find the average of 3 (from (i)) and 4.666 (from (iii))


(3+4.666)/2 = 3.833

            
 Hence, 3.833 is the approximate square root of 14
 

Common Mistakes and How to Avoid Them in the Square Root of 14

When we find the square root of 14, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.

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Problem 1

Simplify 7√14?

Okay, lets begin

7√14

= 7⤬√14

= 7⤬3.741

= 26.187


Answer : 26.187
 

Explanation

√14= 3.741, so multiplying the square root value with 7
 

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Problem 2

What is √14 + √11+ √14 ?

Okay, lets begin

√14+ √11 + √14

= 3.741+3.316+3.741

= 10.798

Answer: 10.798
 

Explanation

 adding the square root value of 14 twice and adding the square root value of 11 with that.
 

Well explained 👍

Problem 3

Find the value of (1/√14)⤬ (1/√14) ?

Okay, lets begin

 (1/√14)⤬ (1/√14)

= 1/14

= 0.0741 


Answer: 0.0741
 

Explanation

 we know, √14⤬√14 = 14 and then solved by dividing 1 by 14

Well explained 👍

Problem 4

If y=√14, find (y²)²

Okay, lets begin

 firstly, y=√14


 Now, squaring y, we get, 


y2= (√14)2=14


Again, do the square of y2

(y2)2=(14)2= 196


Answer : 196
 

Explanation

squaring “y” which is same as squaring the value of √14 resulted to 14. Again, squaring 14 resulted to 196.
 

Well explained 👍

Problem 5

Find √14 / √9

Okay, lets begin

 √14/√9

= √(14/9)

= 3.741/3

= 1.247


Answer : 1.247
 

Explanation

dividing the square root value of 14 with that of square root value of 9.We conclude that, the square root of 14 is derived by multiplying 3.74165738677  with itself, i.e.,  3.74165738677 ╳   3.74165738677. The relation between square and square root is that they are inverse of each other. 
 

Well explained 👍

FAQs on 14 Square Root

1.How to solve √13 ?

√13 can be solved by some methods to yield the square root value, namely, Long Division Method, Prime Factorization Method or Approximation Method.
 

2.What is the cube root of 14 ?

2.4101… is the cube root of 14. 
 

3.Is 14 a perfect square or non-perfect square?

14 is a non-perfect square, since 14 =(3.74165738677) 2.

4.Is the square root of 14 a rational or irrational number?

The square root of 14 is ±3.74165738677. So, 3.74165738677 is an irrational number, since it cannot be obtained by dividing two integers and cannot be written in the form p/q, where p and q are integers.
 

5. What is the square of √14?

6.Is √14 a real number?

Important Glossaries for Square Root of 14

  • 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

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Jaskaran Singh Saluja

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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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