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Square Root of 544

The square root of 544 is expressed as √544 in the radical form and as (544)^½ or (544)^0.5 in the exponent form. The square root of 544 rounded up to 7 decimal places is 23.3238076. It is the positive solution of the equation x² = 544. We can express the square root of 544 in its lowest radical form as 4 √34.

Square Root of 544: 23.323807579381203
Square Root of 544 in exponential form: (544)^½ or (544)^0.5
Square Root of 544 in radical form: √544 or 4 √34

1.	What Is the Square Root of 544?
2.	Is Square Root of 544 Rational or Irrational?/a>
3.	How to Find the Square Root of 544?
4.	Important Notes on Square Root of 544
5.	FAQs on Square Root of 544

What is the Square Root of 544?

The square root of 544 in decimal form is 23.3238.
The square root of 544 is represented as √544 in radical form.
The square root of 544 is represented as (544)^1/2 in exponential form.

Is Square Root of 544 Rational or Irrational?

A rational number is defined as numbers that can be expressed in the form of p/q where q ≠ 0. And the square root of 544 cannot be written in the form of p/q. Thus, the square root of 544 is an irrational number.

How to Find the Square Root of 544?

Square Root of 544 Using Prime Factorization Method

Prime factorization of 544: 2² × 17
Prime factors of 544 in pairs: (2 × 2) × (2 × 2) × 2 × 17
Square root of 544: √544 = √((2 × 2)² × 2 × 17) = (2 × 2)√(2 × 17) = 4√34

Square Root of 544 By Long Division

Start dividing the digits from the right side into pairs of two by drawing a line on top of them. In the case of 544, we have two pairs 24 and 2.
Now, find a number(a) whose square is ≤ 5. The value of a will be 2 as 2 × 2 = 4 ≤ 5.
We get the quotient as 2 and the remainder as 1. Now, add the divisor (a) with itself and get the new divisor 2a (4).
Drag down the next pair (new dividend becomes 144) and calculate a number (N) such that 4N × N ≤ 144. The value of N comes 3.
Now, add a decimal in the dividend (544) and quotient (23) simultaneously. Also, add 3 pairs of zero in the dividend after the decimal (544. 00 00 00) and repeat the above step for the remaining pair of zero.

So, we get the value of the square root of √544 = 23.323 by the long division method.

Square root of 544

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Important Notes:

The number 544 is not a perfect square.
The square root of 544 is an irrational number.
The square root of -544 is an imaginary number.

Square Root of 544 Solved Examples

Example 1: By which smallest number 544 must be multiplied to make it a perfect square?

Solution:
To make 544 a perfect square we have to make the power of 2 and 17 an even number in the prime factorization of 544. And the prime factorization of 544: 2⁵ × 17. So, to make it a perfect square we have to multiply by (2 and 17) 34. Now the power of 2 and 17 are an even number thus, making it a perfect square.
Example 2: Bob is making a square-shaped field with an area of 544 square yards. And the cost of fencing per yard is $√170. How much will it cost Bob to do fencing on three sides of the field?

Solution:
Area of the field = 544 square yards
Length of one side of the field = √544 = 4√34 yards.
Now, the length of the field in which fencing is to done = 3 × length of one side = 3 × 4√34 = 12√34
Cost for fencing will be = 12√34 × Cost of fencing per yard = 12√34 × √170 = 12 × 34√5 = $408√5 = $912.31.

Hence, the cost of fencing three sides of field will cost Bob $912.31.
Example: If the area of a circle is 544π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 544π in²
⇒ r = ±√544 in
Since radius can't be negative,
⇒ r = √544
The square root of 544 is 23.324.
⇒ r = 23.324 in

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FAQs on the Square Root of 544

What is the Value of the Square Root of 544?

The square root of 544 is 23.3238.

Why is the Square Root of 544 an Irrational Number?

Upon prime factorizing 544 i.e. 2⁵ × 17¹, 2 is in odd power. Therefore, the square root of 544 is irrational.

What is the Square Root of 544 in Simplest Radical Form?

We need to express 544 as the product of its prime factors i.e. 544 = 2 × 2 × 2 × 2 × 2 × 17. Therefore, √544 = √2 × 2 × 2 × 2 × 2 × 17 = 4 √34. Thus, the square root of 544 in the lowest radical form is 4 √34.

What is the Value of 9 square root 544?

The square root of 544 is 23.324. Therefore, 9 √544 = 9 × 23.324 = 209.914.

What is the Square of the Square Root of 544?

The square of the square root of 544 is the number 544 itself i.e. (√544)² = (544)^2/2 = 544.

What is the Square Root of -544?

The square root of -544 is an imaginary number. It can be written as √-544 = √-1 × √544 = i √544 = 23.323i
where i = √-1 and it is called the imaginary unit.

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