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.
You are watching: Square root of 27 in radical form
Let us see what the square root of 27 is.
Square Root of 27: √27 = 5.196152Square 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?|
|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 271/2. 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 integersq 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 squaresBy 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 = 101Step 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
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 271/2.The decimal representation of √27 is 5.196125….
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?