Square Root of 14
The symbol of square root is written as √ and is an integral part of mathematics. Once you understand the basics of finding the square root of a number, you can solve any square rootrelated problem. Today, let us find the square root of 14, and explore the answer to questions like, is the square root of 14 a rational number and the square root of 14 in radical form.
 Square Root of 14: √14 = 3.74165
 Square of 14: 14^{2} = 196
What Is the Square Root of 14?
4 can be expressed as 2^{2} = 2 × 2. Here 2 is called the square root of 4 and we know that 4 is a perfect square. Nonsquare numbers also have a square root, the only difference is that they are not whole numbers.
Similarly the square root of 14 is expressed as √14 in the radical form and as 14^{½} in the exponent form. The square root of 14 rounded to 5 decimal places is +3.74165, 3.74165.
Is the Square Root of 14 Rational or Irrational?
A number that cannot be expressed as a ratio of two integers is an irrational number. The decimal form of the irrational number is nonterminating (i.e., it never ends) and nonrecurring (i.e., the decimal part of the number never repeats a pattern). Now let us look at the square root of 14.
√14 = 3.74165738677.
Do you think the decimal part stops after 3.74165738677? No, it is neverending and you cannot notice a pattern in the decimal part.
Hence, √14 is an irrational number.
How to Find the Square Root of 14?
Square Root of 14 By Long Division
The value of the square root of 14 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
 Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 14. So, the number is 3. Putting the divisor as 3, we get the quotient as 3 and the remainder as 5
 Step 3: Double the quotient and enter it with a blank on its right. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder.
 Repeat this process to get the decimal places you want.
The image shows step by step long division method to find the square root of 14
Can you try and express the square root of 15 in a similar way? The answer of √15 should be 3.872.
Simplified Radical Form
To simplify the square root of 14, let us first express 14 as a product of its prime factors. The prime factorization of 14 = 2 × 7. Therefore, √14 is in the lowest form and cannot be simplified further. Thus, we have expressed the square root of 14 in the radical form.
Explore Square roots using illustrations and interactive examples
Think Tank:
 Can you think of a quadratic equation which has a root as √14?
 Since ((√14)^{2}=14, can we say that √14 is also a square root of 14?
Important Notes:
 The square root of 14 is expressed as √14 in the radical form.
 In the exponent form, the square root of 14 is expressed as 14^{½}.
 The real roots of √14 are ±3.74165.
Square Root of 14 Solved Examples

Example 1: Allan told his friends that the value of √14 is same as the value of √14. What do you think?
Solution
Negative square root cannot be real numbers. √14 is a real number. But √ 14 is an imaginary number. Hence, they are not the same.
√14 and √14 are not same.

Example 2: Joel had a doubt. He knew that 6.403 is the square root of 14 but wanted to know if 6.403 is also a square root of 14? Can you help him?
Solution:
Let us take an example of a perfect square number and extend the same logic to clarify her doubt. We know that 3 is a square root of 9 because when 3 is multiplied to itself it gives 9. But what about 3? As, 3 × 3 = 9. Therefore, 3 is also a square root of 9. Going by the same logic, 3.741 is the square root of 14.
FAQs On Square Root of 14
What is the square root of 14?
The square root of 14 is √14 = 3.74165
What is the square of 14?
The square of 14 is 196.
How do you work out the square root of 14?
We can find the square root of 14 using various methods.
 Repeated Subtraction
 Prime Factorization
 Estimation and Approximation
 Long Division
If you want to learn more about each of these methods, click here.
Is square root of 14 a real number?
Yes, square root of 14 is a real number
What is the square root of 14 in the simplest radical form?
√14 is the simplest radical form.
Is the square root of 14 an irrational number?
The square root of 14 is √14 = 3.74165. √14 is an irrational number.