Square Root of 567
The square root of 567 is expressed as √567 in the radical form and as (567)^{½} or (567)^{0.5} in the exponent form. The square root of 567 rounded up to 8 decimal places is 23.81176180. It is the positive solution of the equation x^{2} = 567. We can express the square root of 567 in its lowest radical form as 9 √7.
 Square Root of 567: 23.811761799581316
 Square Root of 567 in exponential form: (567)^{½} or (567)^{0.5}
 Square Root of 567 in radical form: √567 or 9 √7
1.  What is the Square Root of 567? 
2.  How to find the Square Root of 567? 
3.  Is the Square Root of 567 Irrational? 
4.  FAQs 
What is the Square Root of 567?
The square root of 567, (or root 567), is the number which when multiplied by itself gives the product as 567. Therefore, the square root of 567 = √567 = 9 √7 = 23.811761799581316.
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How to Find Square Root of 567?
Value of √567 by Long Division Method
Explanation:
 Forming pairs: 05 and 67
 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 67, to the right of the remainder 1. The new dividend is now 167.
 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 <= 167. After finding Z, together 4 and Z (3) form a new divisor 43 for the new dividend 167.
 Divide 167 by 43 with the quotient as 3, giving the remainder = 167  43 × 3 = 167  129 = 38.
 Now, let's find the decimal places after the quotient 23.
 Bring down 00 to the right of this remainder 38. The new dividend is now 3800.
 Add the last digit of quotient to divisor i.e. 3 + 43 = 46. To the right of 46, find a digit Z (which is 8) such that 46Z × Z <= 3800. Together they form a new divisor (468) for the new dividend (3800).
 Divide 3800 by 468 with the quotient as 8, giving the remainder = 3800  468 × 8 = 3800  3744 = 56.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 567.
Therefore, the square root of 567 by long division method is 23.8 approximately.
Is Square Root of 567 Irrational?
The actual value of √567 is undetermined. The value of √567 up to 25 decimal places is 23.81176179958131531451454. Hence, the square root of 567 is an irrational number.
☛ Also Check:
 Square Root of 44  √44 = 6.63325
 Square Root of 56  √56 = 7.48331
 Square Root of 325  √325 = 18.02776
 Square Root of 225  √225 = 15
 Square Root of 13  √13 = 3.60555
 Square Root of 85  √85 = 9.21954
 Square Root of 105  √105 = 10.24695
Square Root of 567 Solved Examples

Example 1: Solve the equation x^{2} − 567 = 0
Solution:
x^{2}  567 = 0 i.e. x^{2} = 567
x = ±√567
Since the value of the square root of 567 is 23.812,
⇒ x = +√567 or √567 = 23.812 or 23.812. 
Example 2: If the area of an equilateral triangle is 567√3 in^{2}. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a^{2} = 567√3 in^{2}
⇒ a = ±√2268 in
Since length can't be negative,
⇒ a = √2268 = 2 √567
We know that the square root of 567 is 23.812.
⇒ a = 47.624 in 
Example 3: If the area of a square is 567 in^{2}. Find the length of the side of the square.
Solution:
Let 'a' be the length of the side of the square.
⇒ Area of the square = a^{2} = 567 in^{2}
⇒ a = ±√567 in
Since length can't be negative,
⇒ a = √567 = 23.812 in
FAQs on the Square Root of 567
What is the Value of the Square Root of 567?
The square root of 567 is 23.81176.
Why is the Square Root of 567 an Irrational Number?
Upon prime factorizing 567 i.e. 3^{4} × 7^{1}, 7 is in odd power. Therefore, the square root of 567 is irrational.
If the Square Root of 567 is 23.812. Find the Value of the Square Root of 5.67.
Let us represent √5.67 in p/q form i.e. √(567/100) = 5.67/10 = 2.381. Hence, the value of √5.67 = 2.381
What is the Square Root of 567?
The square root of 567 is an imaginary number. It can be written as √567 = √1 × √567 = i √567 = 23.811i
where i = √1 and it is called the imaginary unit.
What is the Value of 1 square root 567?
The square root of 567 is 23.812. Therefore, 1 √567 = 1 × 23.812 = 23.812.
What is the Square of the Square Root of 567?
The square of the square root of 567 is the number 567 itself i.e. (√567)^{2} = (567)^{2/2} = 567.