Square Root of 521
The square root of 521 is expressed as √521 in the radical form and as (521)^{½} or (521)^{0.5} in the exponent form. The square root of 521 rounded up to 6 decimal places is 22.825424. It is the positive solution of the equation x^{2} = 521.
 Square Root of 521: 22.825424421026653
 Square Root of 521 in exponential form: (521)^{½} or (521)^{0.5}
 Square Root of 521 in radical form: √521
1.  What is the Square Root of 521? 
2.  How to find the Square Root of 521? 
3.  Is the Square Root of 521 Irrational? 
4.  FAQs 
What is the Square Root of 521?
The square root of 521, (or root 521), is the number which when multiplied by itself gives the product as 521. Therefore, the square root of 521 = √521 = 22.825424421026653.
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How to Find Square Root of 521?
Value of √521 by Long Division Method
Explanation:
 Forming pairs: 05 and 21
 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 21, to the right of the remainder 1. The new dividend is now 121.
 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 2) such that 4Z × Z <= 121. After finding Z, together 4 and Z (2) form a new divisor 42 for the new dividend 121.
 Divide 121 by 42 with the quotient as 2, giving the remainder = 121  42 × 2 = 121  84 = 37.
 Now, let's find the decimal places after the quotient 22.
 Bring down 00 to the right of this remainder 37. The new dividend is now 3700.
 Add the last digit of quotient to divisor i.e. 2 + 42 = 44. To the right of 44, find a digit Z (which is 8) such that 44Z × Z <= 3700. Together they form a new divisor (448) for the new dividend (3700).
 Divide 3700 by 448 with the quotient as 8, giving the remainder = 3700  448 × 8 = 3700  3584 = 116.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 521.
Therefore, the square root of 521 by long division method is 22.8 approx.
Is Square Root of 521 Irrational?
The actual value of √521 is undetermined. The value of √521 up to 25 decimal places is 22.82542442102665481124372. Hence, the square root of 521 is an irrational number.
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 Square Root of 841  √841 = 29
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Square Root of 521 Solved Examples

Example 1: Solve the equation x^{2} − 521 = 0
Solution:
x^{2}  521 = 0 i.e. x^{2} = 521
x = ±√521
Since the value of the square root of 521 is 22.825,
⇒ x = +√521 or √521 = 22.825 or 22.825. 
Example 2: If the surface area of a sphere is 2084π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 2084π in^{2}
⇒ r = ±√521 in
Since radius can't be negative,
⇒ r = √521
The square root of 521 is 22.825.
⇒ r = 22.825 in 
Example 3: If the area of a square is 521 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} = 521 in^{2}
⇒ a = ±√521 in
Since length can't be negative,
⇒ a = √521 = 22.825 in
FAQs on the Square Root of 521
What is the Value of the Square Root of 521?
The square root of 521 is 22.82542.
Why is the Square Root of 521 an Irrational Number?
The number 521 is prime. This implies that the number 521 is pairless and is not in the power of 2. Therefore, the square root of 521 is irrational.
If the Square Root of 521 is 22.825. Find the Value of the Square Root of 5.21.
Let us represent √5.21 in p/q form i.e. √(521/100) = 5.21/10 = 2.283. Hence, the value of √5.21 = 2.283
Is the number 521 a Perfect Square?
The number 521 is prime. This implies that the square root of 521 cannot be expressed as a product of two equal integers. Therefore, the number 521 is not a perfect square.
Evaluate 18 plus 18 square root 521
The given expression is 18 + 18 √521. We know that the square root of 521 is 22.825. Therefore, 18 + 18 √521 = 18 + 18 × 22.825 = 18 + 410.858 = 428.858
What is the Square Root of 521?
The square root of 521 is an imaginary number. It can be written as √521 = √1 × √521 = i √521 = 22.825i
where i = √1 and it is called the imaginary unit.