Square Root of 54
We all know that the length of each side of a square is the square root of its area. Think of a number that gives 54 on squaring? n^{2 }= 54. What could be n? Squares and square roots are special exponents. When the exponent on the number is 2, it is termed as square and when the exponent is ½ it is called a square root of a number. Let's see how to find the square root of 54 and also discover interesting facts around them. In this mini lesson, let us learn about the square root of 54, find out whether the square root of 54 is rational or irrational, and see how to find the square root of 54 by long division method.
 Square Root of 54: √54 = 7.348
 Square of 54: 54^{2} = 2916
What Is the Square Root of 54?
The square root of a number is the number that is multiplied to itself to give the product as the original number. Nonsquare numbers also have square root, just that they are not whole numbers. 54 is a nonsquare number.
 Square root of 54 in radical form is expressed as √54 and in the exponent form it is expressed as 54^{1/2}
 We can also express the square root of 54 in its lowest radical form as 3√6
 The square root of 54 in the decimal form up to three decimal places = + 7.348 or 7.348
Is Square Root of 54 Rational or Irrational?
A number that cannot be expressed as a ratio of two integers is an irrational number. The decimal form of the irrational number will be nonterminating (i.e it never ends) and nonrecurring (i.e the decimal part of the number never repeats a pattern). Now let us look at the square root of 54. √54 = 7.348. The decimal part is neverending, and we cannot see a pattern in the decimal part. So √54 is an irrational number.
How to Find the Square Root of 54?
There are two different methods to find the square root of 54
 By prime factorization method
 Long division method
Square root of 54 by prime factorization method.
To find the square root of 54, let us first express 54 as a product of its prime factors. The prime factorization of 54 = 2 × 3 × 3 × 3. Therefore, √54 =√( 2 × 3^{3}) = 3√6 and 3√6 = 7.348
Square Root of 54 by Long Division Method
Let us follow the steps to find the square root of 54 by long division.
 Step 1: Make a pair of digit (by placing a bar over it ) from one's place.
 Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 54. We know that 7 × 7 is 49 and is less than 54. Now let us divide 54 by 7
 Step 3: Let us place a decimal point and pairs of zeros and continue our division. Now, multiply the quotient by 2 and the product becomes the starting digit of our next divisor.
 Step 4: Choose a number in the unit's place for the new divisor such that its product with a number is less than or equal to 500. We know that 3 is in the ten's place and our product has to be 500 and the closest multiplication is 143 × 3 = 429. So our long division now looks like:
Explore Square roots using illustrations and interactive examples
Important Notes
 The square root of 54 ≈ 7.348
 The square root of 54 in its simplest radical form is 3√6
 √54 is irrational. Its real roots are +7.348 and 7.348
Challenging Questions
 What is the value of √(√(√(√(54)))?
 Simplify ( (50)^{1/2})^{1/2}
Square Root of 54 Solved Examples

Example 1: Tim said that the value of √54 is same as √54. What do you think?
Solution:
Negative square root cannot have real roots.
√54 has real roots. But √54 has only imaginary roots.
Hence they are not the same. 
Example 2: Joel had a doubt. He knew that 7.348 is a square root of 54. He wanted to know if 7.348 is also a square root of 54? Can you clarify his doubt?
Solution:
Let us take an example of a perfect square number and extend the same logic to clarify her doubt. We know that 5 is a square root of 25 because when 5 is multiplied to itself it gives 25
But what about 5? Let us multiply and check.
5 × 5 = 25, because ( ×  = +). Therefore 5 is also a square root of 25
Going by the same logic,7.348 is also the square root of 54.
FAQs On Square Root of 54
What is the square root of 54?
The value of √54 = 7.348 approximated to 2 decimal places.
How do you simplify square root of 54?
3√6 is the simplest form of √54.
54 is the square root of which number?
54 is the square root of 2916.
Is √54 a rational number?
√54 is an irrational number, because the value of √54 is a nonteminating decimal.
How to find the square root of 54?
√54 can be accurately evaluated using the long division method.
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