We all know that the length of each side of a square is the square root of its area. Think of a number that provides 54 on squaring? n2= 54. What could be n? Squares and square roots are unique exponents. When the exponent on the number is 2, it is termed as square and also when the exponent is ½ it is referred to as a square root of a number. Let's watch how to uncover the square root of 54 and likewise find interesting facts approximately them. In this mini leschild, let us learn about the square root of 54, find out whether the square root of 54 is rational or irrational, and check out just how to find the square root of 54 by long division method.

You are watching: Square root of 54 in radical form

**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 |

6. | Challenging Questions |

## What Is the Square Root of 54?

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

We have the right to also express the square root of 54inits lowest radical develop as 3**√**6The square root of 54 in the decimal form up to 3 decimal places = + 7.348 or -7.348

## Is Square Root of 54 Rational or Irrational?

A number that cannot be expressed as a proportion of two integers is an irrational number.The decimal develop of the irrational number will certainly 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 component is never-finishing, and also we cannot see a pattern in the decimal part.So **√**54 is an irrational number.

## How to Find the Square Root of 54?

Tbelow are two various methods to discover the square root of 54

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

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

### Square Root of 54 by Long Division Method

Let us follow the actions to find the square root of 54by lengthy department.

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Explore Square roots making use of illustrations and also interactive examples

**Important Notes**

The square root of 54 ≈ 7.348The square root of 54 in its simplest radical create is 3

**√**6

**√**54 is irrational. Its genuine roots are +7.348 and also -7.348

**Challenging Questions**

What is the value of

**√**(

**√**(

**√**(

**√**(54)))?Simplify ( (50)1/2)1/2

**Example 2:**Joel had a doubt. He kbrand-new that 7.348is a square root of 54. He wanted to understand 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 also extend the very same logic to clarify her doubt.We know that 5is a square root of 25because as soon as 5is multiplied to itself it gives 25But what around -5?Let us multiply and check.-5 × -5= 25, because (- × - = +).Therefore -5is likewise a square root of 25Going by the exact same logic,-7.348 is likewise the square root of 54.