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? n2= 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.

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**Square Root of 54**:**√**54 = 7.348**Square of 54: **542 = 2916

1. | What Is the Square Root of 54? |

2. | Is Square Root of 54 Rational or Irrational? |

3. | How to Find the Square Root of 54? |

4. | FAQs on Square Root of 54 |

5. | Important Notes on Square Root of 54 |

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Challenging Questions |

## What Is the Square Root of 54?

Thesquare root of a number is the number that ismultiplied to itself to give the product as the original number. Non-square numbers also have square root, just that they are not whole numbers. 54 is a non-square number.

We can also express the square root of 54inits lowest radical form as 3**√**6The 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 non-terminating (i.e it never ends) and non-recurring (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 never-ending, 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

### Square root of 54 by prime factorization method.

To findthe square root of 54, let us first express 54as a product of its prime factors.The **prime factorization of 54= 2 × 3× 3 × 3**. Therefore,**√**54 =**√**(2 × 33) = 3**√**6 and3**√**6= 7.348

### Square Root of 54 by Long Division Method

Let us follow the steps to find the square root of 54by long division.

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Step 1:Make a pair of digit (by placing a bar over it ) from one'splace.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× 7is 49 and is less than 54. Now let us divide 54by 7Step 3: Let us place a decimal point andpairs 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 anumber 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 3is in the ten's place and our product has to be 500 and the closest multiplication is143× 3= 429. So our long division now looks like:

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**Important Notes**

The square root of 54 ≈ 7.348The 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

**Example 2:**Joel had a doubt. He knew that 7.348is 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 5is a square root of 25because when 5is multiplied to itself it gives 25But what about -5?Let us multiply and check.-5 × -5= 25, because (- × – = +).Therefore -5is also a square root of 25Going by the same logic,-7.348 is also the square root of 54.