Square Root of 27

In Mathematics, the square root of 27 is a number, which when multiplied by itself, should produce the result 27. The number 27 is a composite number, as it has more than two factors. In this article, we are going to discuss the value of the square root of 27, and also learn how to find the square root of 27 using the long division method and prime factorization method with complete explanation.

Table of Contents:

• What Is The Square Root Of 27?
• Square Root Of 27 In Radical Form
• Square Root Of 27 By Prime Factorization Method
• Square Root Of 27 By Long Division Method
• Examples
• FAQs

What is the square Root of 27?

The square root of 27 is a number, which when multiplied by itself gives the original number 27. The square root of 27 is symbolically represented as √27.

(i.e) = √27 = √(Number × Number)

Thus, if we multiply the number 5.1961, we will get the number 27.

Therefore, √27 = √(5.1961 × 5.1961)

√27 = √(5.1961)²

Now, remove square and square root on the right-hand side, we get

√27 = ± 5.1961.

Square Root of 27 in Radical Form

The square root of 27 can also be represented in the radical form. Since 27 is a perfect cube number, the number 27 is written as 3 × 3 × 3. Thus, the square root of 27 in radical form is written as follows:

√27 = √(3 × 3 × 3)

√27 = √(3) ×√(3)²

√27 = 3√3.

Therefore, the square root of 27 in radical form is 3√3.

Square Root of 27 by Prime Factorization Method

The square root of 27 can be found using two different methods, such as the prime factorization method and the long division method. Now, let us discuss the prime factorization method to find the square root of 27.

Let us consider the prime factorization of 27, 3³, which is equal to 3 × 3 × 3.

Thus, √27 = √(3 × 3 × 3) = 3√3, which is the radical form of the square root of 27.

To obtain the square root of 27 in decimal form, substitute the approximate value of the square root of 3 in the radical form.

Thus, √27 = 3√3 = 3 × 1.732

√27 = 5.196.

Therefore, the value of the square root of 27 in decimal form is 5.196 (approximately).

Square Root of 27 by Long Division Method

The value of the square root of 27 can be exactly found using the long division method. Generally, the long division method is used to find the value of the square root of a number, when a number is a non-perfect square number. Now, let us discuss how to find the value of the square root of 27 using the long division method.

Step 1: Write the number 27 in decimal form. To find the exact value of the square root of 27, add 6 zeros after the decimal point. Hence, 27 in decimal form is 27. 000000. Now, pair the number 27 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 27 by a number, such that the product of the number (i.e. number×number) should be less than or equal to 27. Thus, 5×5 =25, which is less than 27. Thus, we obtained the quotient = 5 and remainder = 2.

Step 3: Double the quotient value, so we get 10, and assume that 100 is the new divisor. Now, bring down the value 00 for division operation. So, the new dividend obtained is 200. Now, find the number, such that (100 + new number) × new number should give the product value, that should be less than or equal to 200. Hence, (100+1) × 1 = 101, which is less than 200.

Step 4: Now subtract 101 from 200, and we get 99 as the new remainder, and 51 as a quotient.

Step 5: The new quotient obtained is 51, and double that. Hence, we get 102 and assume that 1020 is our new divisor. Now, bring down the two zeros and, and we have 9900 as the new dividend.

Step 6: Find the number, such that (1020 + new number) × new number should give the product value that should be less than or equal to 9900. Thus, (1020+9) × 9 = 9261, which is less than 9900.

Step 7: Subtract 9261 from 9900, and we get 639 as the new reminder.

Step 8: Continue this process until we get the approximate value of the square root of 27 upto 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 27, √27 is 5.196.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify: (√3√27) + 9

Solution:

Given: (√3√27) + 9 …(1)

We know that the square root of 27 in radical form is 3√3.

Now, substitute √27 = 3√3 in (1) we get,

(√3√27) + 9 = (√3. 3√3)+9

(√3√27) + 9 = 9 + 9

(√3√27) + 9 = 18

Therefore, (√3√27) + 9 = 18.

Example 2:

Simplify: 10√27.

Solution:

Given: 10√27.

We know that the square root of 27 in decimal form is 5.196

Therefore, 10√27 = 10(5.196)

10√27 = 51.96

Therefore, 10√27 is 51.96.