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Square Root of 14

The square root of 14 is expressed as √14 in the radical form and as (14)^½ or (14)^0.5 in the exponent form. The square root of 14 rounded up to 5 decimal places is 3.74166. It is the positive solution of the equation x² = 14.

Square Root of 14: 3.7416573867739413
Square Root of 14 in exponential form: (14)^½ or (14)^0.5
Square Root of 14 in radical form: √14

1.	What Is the Square Root of 14?
2.	Is Square Root of 14 Rational or Irrational?
3.	How to Find the Square Root of 14?
4.	Thinking Out of the Box!
5.	Important Notes on Square Root of 14
6.	FAQs on Square Root of 14

What Is the Square Root of 14?

4 can be expressed as 2² = 2 × 2. Here 2 is called the square root of 4 and we know that 4 is a perfect square. Non-square 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 non-terminating (i.e., it never ends) and non-recurring (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 never-ending 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.

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.
Example: If the area of an equilateral triangle is 14√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 14√3 in²
⇒ a = ±√56 in
Since length can't be negative,
⇒ a = √56 = 2 √14
We know that the square root of 14 is 3.742.
⇒ a = 7.483 in

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FAQs on the Square Root of 14

What is the Value of the Square Root of 14?

The square root of 14 is 3.74165.

Why is the Square Root of 14 an Irrational Number?

Upon prime factorizing 14 i.e. 2¹ × 7¹, 2 is in odd power. Therefore, the square root of 14 is irrational.

What is the Value of 15 square root 14?

The square root of 14 is 3.742. Therefore, 15 √14 = 15 × 3.742 = 56.125.

What is the Square Root of -14?

The square root of -14 is an imaginary number. It can be written as √-14 = √-1 × √14 = i √14 = 3.741i
where i = √-1 and it is called the imaginary unit.

Evaluate 15 plus 6 square root 14

The given expression is 15 + 6 √14. We know that the square root of 14 is 3.742. Therefore, 15 + 6 √14 = 15 + 6 × 3.742 = 15 + 22.450 = 37.450

If the Square Root of 14 is 3.742. Find the Value of the Square Root of 0.14.

Let us represent √0.14 in p/q form i.e. √(14/100) = 0.14/10 = 0.374. Hence, the value of √0.14 = 0.374

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