Square Root Of 54 Simplified

Square Root of 54

We all know that the length of each side of a square is the square root of its surface area. Think of a number that gives 54 on squaring? due north²= 54. What could exist n? Squares and square roots are special exponents. When the exponent on the number is 2, it is termed equally square and when the exponent is ½ it is called a square root of a number. Let's run into how to find the foursquare root of 54 and besides find interesting facts around them. In this mini lesson, let us acquire about the square root of 54, discover out whether the square root of 54 is rational or irrational, and see how to detect the square root of 54 past long division method.

Square Root of 54: √54 = seven.348
Square of 54: 54² = 2916

i.	What Is the Square Root of 54?
2.	Is Square Root of 54 Rational or Irrational?
3.	How to Find the Foursquare Root of 54?
4.	FAQs on Square Root of 54
v.	Important Notes on Square Root of 54
6.	Challenging Questions

What Is the Square Root of 54?

The square root of a number is the number that is multiplied to itself to give the production as the original number. Non-foursquare numbers also have square root, just that they are not whole numbers. 54 is a non-square number.

Square root of 54 in radical form is expressed as √54 and in the exponent class it is expressed as 54^1/2
We tin can also express the foursquare root of 54 in its everyman radical form equally 3√6
The square root of 54 in the decimal form upward to 3 decimal places = + 7.348 or -seven.348

Is Square Root of 54 Rational or Irrational?

A number that cannot exist expressed every bit a ratio of two integers is an irrational number. The decimal grade of the irrational number will be non-terminating (i.eastward it never ends) and non-recurring (i.e the decimal office of the number never repeats a design). At present let u.s.a. look at the square root of 54.√54 = 7.348. The decimal office is never-ending, and nosotros cannot see a blueprint in the decimal part. So √54 is an irrational number.

How to Discover the Square Root of 54?

There are two unlike methods to find the square root of 54

Past prime factorization method
Long division method

Square root of 54 by prime factorization method.

To find the square root of 54, let usa first express 54 as a production of its prime factors. The prime factorization of 54 = 2 × 3 × 3 × iii. Therefore,√54 =√( 2 × three³) = 3√6 and 3√6 = 7.348

Square Root of 54 by Long Division Method

Allow us follow the steps to find the foursquare root of 54 by long division.

Pace ane: Make a pair of digit (by placing a bar over it ) from one's identify.
Step 2: Detect a number such that when you multiply information technology with itself, the production is less than or equal to 54. We know that vii × 7 is 49 and is less than 54. At present permit united states of america divide 54 by 7
Stride 3: Let us identify a decimal betoken and pairs of zeros and continue our division. Now, multiply the caliber 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'south place and our product has to be 500 and the closest multiplication is 143 × 3 = 429. So our long division at present looks like:

finding square root of 54 using-division-method

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Of import 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)^ane/ii)^ane/two

Case ane: Tim said that the value of√54 is same equally √-54. What exercise yous think?

Solution:

Negative foursquare root cannot take real roots.
√54 has real roots. Just √-54 has only imaginary roots.
Hence they are not the same.
Instance ii:Joel had a incertitude. He knew that vii.348 is a square root of 54. He wanted to know if -7.348 is as well a square root of 54? Tin y'all analyze his doubt?

Solution:

Permit 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 five is multiplied to itself it gives 25
Merely what nearly -5? Let united states of america multiply and cheque.
-5 × -v = 25, because (- × - = +). Therefore -v is also a square root of 25
Going by the same logic,-7.348 is also the square root of 54.

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FAQs On Square Root of 54

What is the square root of 54?

The value of√54 = vii.348 approximated to ii decimal places.

How exercise y'all simplify foursquare root of 54?

3√half-dozen is the simplest course 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 not-teminating decimal.

How to find the square root of 54?

√54 can be accurately evaluated using the long sectionalization method.