Square Root of 14

In Mathematics, the square root of 14 is a number, if it is multiplied by itself and results in the original number 14. The square root of 14 is an irrational number since it cannot be expressed in the form of p/q and the decimal part of the value of the square root of 14 is a non-repeating and non-terminating number. In this article, we will learn the value of the square root of 14 and the two different methods that help to find the square root of 14, such as the prime factorization method and the long division method are discussed in detail.

Table of Contents:

• What Is The Square Root Of 14?
• Square Root Of 14 In Radical Form
• Square Root Of 14 By Prime Factorization Method
• Square Root Of 14 By Long Division Method
• Solved Examples
• FAQs

What is the Square Root of 14?

The 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.

Hence, √14 = √(Number × Number)

Thus, if we multiply the number 3.742 two times, we get the original value 14.

(i.e) √14 = √(3.742× 3.742)

√14 = √(3.742)²

Now, remove square and square root, we get

√14 = ± 3.742 (Rounded to three decimal places)

Square Root of 14 in Radical Form

The value of the square root of 14 can also be expressed in radical form. The radical value of the square root of 14 can be found, if we know the prime factorization of 14. The prime factorization of 14 is 2 × 7. Thus, the square root of 14 in radical form is expressed as follows:

√14 = √(2 × 7)

√14 = √2.√7, which is not the simplest radical form.

Hence, we can say that the square root of 14 in the simplest radical form is √14.

Square Root of 14 by Prime Factorization Method

To find the square root of 14 using the prime factorization method, one must know the prime factorization of 14. We know that the prime factorization of 14 is 2 × 7.

Thus, √14 = √(2 × 7) = √2. √7.

We know that the value of √2 is 1.414 and √7 is 2.646.

Now, substitute the value in the above expression, we get

√14 = 1.414 × 2.646

√14 = 3.742 (approximately)

Hence, the square root of 14 in decimal form is approximately equal to 3.742 (rounded to three decimal places)

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.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify (√14√14) – 5

Solution:

Given: (√14√14) – 5…(1)

(√14√14) – 5 = (√14)² – 5

Now, cancel out square and square root, we get

(√14√14) – 5 = 14 – 5

(√14√14) – 5 = 9

Therefore, (√14√14) – 5 = 9

Example 2:

Find the value of x, if 10x+√14 = 20

Solution:

Given equation: 10x+√14 = 20…(1)

We know that √14 = 3.742.

Now, substitute the value in equation (1),

10x+√14 = 20

10x + 3.742 = 20

10x = 20 – 3.742

10x = 16.258

x = 16.258/10

x = 1.6258

Therefore, the value of x is 1.6258.