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Square Root of 27

Do you know that the number 27 is the only positive integer which is 3 times the sum of its digits? 27 is also called the trinity of trinities because it is the cube of 3. In this chapter, we will calculate the square root of 27 by long division method along with solved examples and interactive questions.
Let us see what the square root of 27 is.

Square Root of 27: √27 = 5.196152
Square of 27: 27² = 729

1.	What Is the Square Root of 27?
2.	Is Square Root of 27 Rational or Irrational?
3.	How to Find the Square Root of 27?
4.	Important Notes
5.	Thinking Out of the Box!
6.	FAQs on Square Root of 27

What Is the Square Root of 27?

The square root of a number is the number that gets multiplied to itself to give the original number. Non-square numbers also have a square root, just that they are not whole numbers. Square root of 27 in the radical form is represented as √27 and in exponent form it is expressed as 27^1/2. The square root of 27 rounded to 6 decimal places is 5.196152.

Is the Square Root of 27 Rational or Irrational?

A rational number is a number that is of the form p/q where:

p and q are integers
q is not equal to 0

A number that cannot be expressed as a ratio of two integers is an irrational number. Non-terminating decimals having repeated numbers after the decimal point are rational numbers. Now let us look at the square root of 27.
√27 = 5.196152.
Do you think the decimal part stops after 5.196152? No, it is never-ending. Therefore, it is a non-terminating decimal with non-repeating numbers.
The number 5.1961524227... can't be written in p/q form. So √27 is an irrational number.

How to Find the Square Root of 27?

Square roots can be calculated using two methods:

By simplifying the radical of the numbers that are perfect squares
By using the long division method for perfect and non-perfect squares

The square of the number 5 is 5 × 5 = 25 and the square of the number 6 is 6 × 6 = 36. The number 27 is lies between 25 and 36, therefore 27 is not a perfect square of an integer. Hence, the long division method is used to evaluate the square root of 27.

Simplified Radical Form of Square Root of 27

To simplify the square root of 27, let us first express 27 as a product of its prime factors. Prime factorization of 27 is 3 × 3 × 3. Therefore, √27 can be simplified further as √3 × 3 × 3 =3√3. Thus, we have expressed the square root of 27 in the simplest radical form as 3√3. Can you try to express the square root of 20 in a similar way?

Square Root of 27 by Long Division Method

Follow the steps given below to find the square root of 27 by long division.

Step 1: Group the digits 2 and 7 into a pair by placing a bar over it. Since our number is 27, let us represent it as inside the division symbol.
Step 2: Find the largest number such that when you multiply it with itself, the product is less than or equal to 27. We know that 5 × 5 = 25 and 25 is less than 27.
Step 3: Let us place a decimal point and zero pairs and continue our division. Now, multiply the quotient by 2 and the product becomes the starting digit of our next divisor.
Step 4: Choose the largest number in the unit's place for the new divisor such that its product with a number is less than or equal to 200. We know that 0 is in the ten's place and our product has to be 200 and the closest multiplication is 102 × 2 = 204. But 204 is greater than 200. Therefore use the number 1 in the unit place which gives 101 × 1 = 101
Step 5: Bring down the next pair of zeros and multiply the quotient 51 (ignore the decimal) by 2, which is 102, and the starting digit of the new divisor. Note that the square root of 27 is an irrational number, i.e., it is never-ending. So, stop the process after 2 or 3 more iterations by repeating steps 3 and 4, and you have the square root of 27 by the long division method.

Explore Square roots using illustrations and interactive examples

Important Notes:

The square root of 27 in the radical form is expressed as 3√3.
In exponent form, the square root of 27 is written as 27^1/2.
The decimal representation of √27 is 5.196125....

Think Tank:

Can you think of a quadratic equation which has its roots as √27?
Since (-√27)²= 27, can we say that -√27 is also a square root of 27?

Square Root of 27 Solved Examples

Example 1: Michael wants to fence his square farm. The area of his square farm is 27 square feet. How many feet of fencing will Michael need?

Solution:

We need to find the square root of 27.
√27 = √3 × 3 × 3 = 3 × √3 = 3√3
So, Michael will need 3√3 feet of fencing for each of the 4 sides. Fencing needed = 4 × 3√3 = 12√3 = 20.78 feet
Hence, Michael will need 20.78 feet of fencing.
Example 2: Sally is enjoying brunch with her family. She has a large square yard of area 27 square feet. Can you help her find the length of her yard?

Solution:

We can write 27 as 27 = 3 × 9
Using the property of square roots, we have √27 =√3 × √9
√37 = √3 × √9 = 3√3 = 5.19 feet
Hence, the length of the yard is 5.19 feet.

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FAQs On Square Root of 27

What is the square root of 27?

The square root of 27 is 3√3.

How do you simplify the square root of 27?

Write 27 as the product of its prime factors. So, 27 = 3 × 3 × 3.
Then, we proceed as follows √27 =√3 × 3 × 3 = 3√3

Is the square root of 27 rational?

No, the square root of 27 is not rational.

What is the square root of 27 rounded to the nearest tenth?

The square root of 27 to the nearest tenth is 5.2.

Is square root of 27 a real number?

Yes, the square root of 27 is a real number.

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