Square Root of 549
The square root of 549 is expressed as √549 in the radical form and as (549)^{½} or (549)^{0.5} in the exponent form. The square root of 549 rounded up to 8 decimal places is 23.43074903. It is the positive solution of the equation x^{2} = 549. We can express the square root of 549 in its lowest radical form as 3 √61.
 Square Root of 549: 23.430749027719962
 Square Root of 549 in exponential form: (549)^{½} or (549)^{0.5}
 Square Root of 549 in radical form: √549 or 3 √61
1.  What is the Square Root of 549? 
2.  How to find the Square Root of 549? 
3.  Is the Square Root of 549 Irrational? 
4.  FAQs 
What is the Square Root of 549?
The square root of 549, (or root 549), is the number which when multiplied by itself gives the product as 549. Therefore, the square root of 549 = √549 = 3 √61 = 23.430749027719962.
ā Check: Square Root Calculator
How to Find Square Root of 549?
Value of √549 by Long Division Method
Explanation:
 Forming pairs: 05 and 49
 Find a number Y (2) such that whose square is <= 5. Now divide 05 by 2 with quotient as 2.
 Bring down the next pair 49, to the right of the remainder 1. The new dividend is now 149.
 Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 3) such that 4Z × Z <= 149. After finding Z, together 4 and Z (3) form a new divisor 43 for the new dividend 149.
 Divide 149 by 43 with the quotient as 3, giving the remainder = 149  43 × 3 = 149  129 = 20.
 Now, let's find the decimal places after the quotient 23.
 Bring down 00 to the right of this remainder 20. The new dividend is now 2000.
 Add the last digit of quotient to divisor i.e. 3 + 43 = 46. To the right of 46, find a digit Z (which is 4) such that 46Z × Z <= 2000. Together they form a new divisor (464) for the new dividend (2000).
 Divide 2000 by 464 with the quotient as 4, giving the remainder = 2000  464 × 4 = 2000  1856 = 144.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 549.
Therefore, the square root of 549 by long division method is 23.4 approximately.
Is Square Root of 549 Irrational?
The actual value of √549 is undetermined. The value of √549 up to 25 decimal places is 23.43074902771996318238917. Hence, the square root of 549 is an irrational number.
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 Square Root of 1296  √1296 = 36
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Square Root of 549 Solved Examples

Example 1: Solve the equation x^{2} − 549 = 0
Solution:
x^{2}  549 = 0 i.e. x^{2} = 549
x = ±√549
Since the value of the square root of 549 is 23.431,
⇒ x = +√549 or √549 = 23.431 or 23.431. 
Example 2: If the area of a circle is 549π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 549π in^{2}
⇒ r = ±√549 in
Since radius can't be negative,
⇒ r = √549
The square root of 549 is 23.431.
⇒ r = 23.431 in 
Example 3: If the surface area of a sphere is 2196π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 2196π in^{2}
⇒ r = ±√549 in
Since radius can't be negative,
⇒ r = √549
The square root of 549 is 23.431.
⇒ r = 23.431 in
FAQs on the Square Root of 549
What is the Value of the Square Root of 549?
The square root of 549 is 23.43074.
Why is the Square Root of 549 an Irrational Number?
Upon prime factorizing 549 i.e. 3^{2} × 61^{1}, 61 is in odd power. Therefore, the square root of 549 is irrational.
Evaluate 7 plus 9 square root 549
The given expression is 7 + 9 √549. We know that the square root of 549 is 23.431. Therefore, 7 + 9 √549 = 7 + 9 × 23.431 = 7 + 210.877 = 217.877
What is the Square of the Square Root of 549?
The square of the square root of 549 is the number 549 itself i.e. (√549)^{2} = (549)^{2/2} = 549.
What is the Square Root of 549?
The square root of 549 is an imaginary number. It can be written as √549 = √1 × √549 = i √549 = 23.43i
where i = √1 and it is called the imaginary unit.
If the Square Root of 549 is 23.431. Find the Value of the Square Root of 5.49.
Let us represent √5.49 in p/q form i.e. √(549/100) = 5.49/10 = 2.343. Hence, the value of √5.49 = 2.343