Square Root of 14

Square Root of 14 is approximately 3.7416 as 3.74 × 3.74 ≈ 14. Square Root of a number is represented as the value of another number when it is multiplied by itself giving the value of as the original number.

Square Root of 14 in mathematical form is written with a radical sign like this √14. The square of 14 in exponential form is written as (14)^1/2 or (14)^0.5.

What is the Square Root of 14?

Square Root of 14 is a number, which when multiplied by itself and results in the number 14. The square root of 14 is symbolically expressed as √14.

√14 = √(Number × Number)

Thus, if we multiply the number two times, we get the original value 14.

√14 ≈ √(3.742× 3.742) = √(3.742)² = 3.742

Root 14 Value

Numerical value of √14 upto 15 decimal place is:

Value of √14: 3.741657386773941 . . .

Square Root of 14 Calculator

How to find square root of 14?

The square root of a number is the value that when multiplied by itself. For example, 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. Perfect Squares are the numbers, the roots of which are whole numbers.

Similarly, we can easily find square root of number like 4,9,25,36,49,64 etc as all these numbers are perfect squares.

To find the square of non-perfect square, in our case to find the square root of 14, we can use the following methods:

• Prime Factorization Method
• Long Division Method

Square Root of 14 by Prime Factorization

To calculate the square root of 14 using the prime factorization method, we need to know the prime factorization of the number 14.

Thus, Prime factorization of 14 is 2 x 7.

And, also we know that the value of √2 is 1.414 and the value of √7 is 2.646.

⇒ √14 = √2 x √7

⇒ √14 = 1.414 x 2.646

⇒ √14 = 3.742

• Square Root of 14 by Prime Factorization: 3.742

Square Root of 14 by Long Division Method

Follow the below steps to find the square root of 14 using the long division method:

Step 1: Write the number 14 in decimal form. To find the exact value of the square root of 14, add 6 zeros after the decimal point. Hence, 14 in decimal form is 14.000000. Now, pair the number 14 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 14 by a number, such that the product of the same number should be less than or equal to 14. Thus, 3×3 =9, which is less than 14. Thus, we obtained the quotient = 3 and remainder = 5.

Step 3: Double the quotient value, so we get 6 and assume that 60 is the new divisor. Now, bring down the value 00 for division operation. So, the new dividend obtained is 500. Now, find the number, such that (60 + new number) × new number should give the product value, that should be less than or equal to 500. Hence, (60+7) × 7 = 469, which is less than 500.

Step 4: Now subtract 469 from 500, and we get 31 as the new reminder, and 37 as a quotient.

Step 5: The new quotient obtained is 37, and double that. Hence, we get 74 and assume that 740 is our new divisor. Now, bring down the two zeros and, we have 3100 as the new dividend.

Step 6: Find the number, such that (740 + new number) × new number should give the product value, that should be less than or equal to 3100. Thus, (740+4)× 4 = 2976, which is less than 3100.

Step 7: Subtract 2976 from 3100, and we get 124 as the new reminder.

Step 8: Continue this process until we get the approximate value of the square root of 14 up to three decimal places. (Note: keep the decimal point in the quotient value after bringing down all the values in the dividend).

Step 9: Thus, the approximate value of the square root of 14, √14 is 3.7416.

Hence, the square root of 14 rounded to three decimal places is 3.742.

Is Square Root 14 an Rational Number?

No, the square root of 14 is not a rational number. A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. The square root of 14 cannot be expressed as a fraction of two integers, so it is an irrational number.

Square Root of 14: FAQs

What is the Square Root of 14?

The Square Root of 14 is 3.741657386773941…

Is the Square Root of 14 Rational Number?

No, the square root of 14 is not a rational number as it has non-terminating and non-repeating decimal expansion.

Is 14 a Perfect Square?

As the number 14 cannot be expressed as the product of two equal integers, 14 is not a perfect square number.

Is 14 a Perfect Cube Number?

No, 14 is not a perfect cube, since it cannot be represented as the product of three equal integers.

Is 14 a Prime Number?

No, the number 14 is not a prime number as it has 2 and 7 as its factors.