Square Root of 481
The square root of 481 is expressed as √481 in the radical form and as (481)^{½} or (481)^{0.5} in the exponent form. The square root of 481 rounded up to 10 decimal places is 21.9317121995. It is the positive solution of the equation x^{2} = 481.
 Square Root of 481: 21.93171219946131
 Square Root of 481 in exponential form: (481)^{½} or (481)^{0.5}
 Square Root of 481 in radical form: √481
1.  What is the Square Root of 481? 
2.  How to find the Square Root of 481? 
3.  Is the Square Root of 481 Irrational? 
4.  FAQs 
What is the Square Root of 481?
The square root of 481, (or root 481), is the number which when multiplied by itself gives the product as 481. Therefore, the square root of 481 = √481 = 21.93171219946131.
☛ Check: Square Root Calculator
How to Find Square Root of 481?
Value of √481 by Long Division Method
Explanation:
 Forming pairs: 04 and 81
 Find a number Y (2) such that whose square is <= 4. Now divide 04 by 2 with quotient as 2.
 Bring down the next pair 81, to the right of the remainder 0. The new dividend is now 81.
 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 1) such that 4Z × Z <= 81. After finding Z, together 4 and Z (1) form a new divisor 41 for the new dividend 81.
 Divide 81 by 41 with the quotient as 1, giving the remainder = 81  41 × 1 = 81  41 = 40.
 Now, let's find the decimal places after the quotient 21.
 Bring down 00 to the right of this remainder 40. The new dividend is now 4000.
 Add the last digit of quotient to divisor i.e. 1 + 41 = 42. To the right of 42, find a digit Z (which is 9) such that 42Z × Z <= 4000. Together they form a new divisor (429) for the new dividend (4000).
 Divide 4000 by 429 with the quotient as 9, giving the remainder = 4000  429 × 9 = 4000  3861 = 139.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 481.
Therefore, the square root of 481 by long division method is 21.9 approximately.
Is Square Root of 481 Irrational?
The actual value of √481 is undetermined. The value of √481 up to 25 decimal places is 21.93171219946130881654807. Hence, the square root of 481 is an irrational number.
☛ Also Check:
 Square Root of 140  √140 = 11.83216
 Square Root of 69  √69 = 8.30662
 Square Root of 21  √21 = 4.58258
 Square Root of 15  √15 = 3.87298
 Square Root of 74  √74 = 8.60233
 Square Root of 35  √35 = 5.91608
 Square Root of 56  √56 = 7.48331
Square Root of 481 Solved Examples

Example 1: Solve the equation x^{2} − 481 = 0
Solution:
x^{2}  481 = 0 i.e. x^{2} = 481
x = ±√481
Since the value of the square root of 481 is 21.932,
⇒ x = +√481 or √481 = 21.932 or 21.932. 
Example 2: If the area of a circle is 481π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 481π in^{2}
⇒ r = ±√481 in
Since radius can't be negative,
⇒ r = √481
The square root of 481 is 21.932.
⇒ r = 21.932 in 
Example 3: If the area of a square is 481 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} = 481 in^{2}
⇒ a = ±√481 in
Since length can't be negative,
⇒ a = √481 = 21.932 in
FAQs on the Square Root of 481
What is the Value of the Square Root of 481?
The square root of 481 is 21.93171.
Why is the Square Root of 481 an Irrational Number?
Upon prime factorizing 481 i.e. 13^{1} × 37^{1}, 13 is in odd power. Therefore, the square root of 481 is irrational.
If the Square Root of 481 is 21.932. Find the Value of the Square Root of 4.81.
Let us represent √4.81 in p/q form i.e. √(481/100) = 4.81/10 = 2.193. Hence, the value of √4.81 = 2.193
Is the number 481 a Perfect Square?
The prime factorization of 481 = 13^{1} × 37^{1}. Here, the prime factor 13 is not in the pair. Therefore, 481 is not a perfect square.
What is the Square Root of 481?
The square root of 481 is an imaginary number. It can be written as √481 = √1 × √481 = i √481 = 21.931i
where i = √1 and it is called the imaginary unit.
What is the Square Root of 481 in Simplest Radical Form?
We need to express 481 as the product of its prime factors i.e. 481 = 13 × 37. Therefore, as visible, the radical form of the square root of 481 cannot be simplified further. Therefore, the simplest radical form of the square root of 481 can be written as √481