Square Root of 20
The square root of 20 is expressed as √20 in the radical form and as (20)^{½} or (20)^{0.5} in the exponent form. The square root of 20 rounded up to 8 decimal places is 4.47213595. It is the positive solution of the equation x^{2} = 20. We can express the square root of 20 in its lowest radical form as 2 √5.
 Square Root of 20: 4.47213595499958
 Square Root of 20 in exponential form: (20)^{½} or (20)^{0.5}
 Square Root of 20 in radical form: √20 or 2 √5
1.  What Is the Square Root of 20? 
2.  Is Square Root of 20 Rational or Irrational? 
3.  How to Find the Square Root of 20? 
4.  Important Notes 
5.  FAQs on Square Root of 20 
6.  Thinking Out of the Box! 
What Is the Square Root of 20?
The square root of 20 can be obtained by the number whose square gives the original number. What number that could be? It can be seen that, there are no integers whose square will give 20.
√20 = 4.472
To check this answer, we can find (4.472)^{2} and we can see that we get the number 19.998784 ... which is very close to 20 when it's rounded to its nearest value.
Is the Square Root of 20 Rational or Irrational?
A rational number is either terminating or nonterminating and has a repeating pattern in its decimal part. We saw that √20 = 4.4721359549. This is nonterminating and the decimal part has no repeating pattern. So it is NOT a rational number. Hence, √20 is an irrational number.
How to Find the Square Root of 20?
There are different methods to find the square root of any number. Click here to know more about it.
Simplified Radical Form of Square Root of 20
20 is not a prime number. Thus it has more than two factors, 1, 2, 4, 5, 10 and 20. To find the square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them. The factorization of 20 is 2 × 2 × 5 which has 1 pair of the same number. Thus, the simplest radical form of √20 is 2√5 itself.
Square Root of 20 by Long Division Method
The square root of 20 can be found using the long division as follows.
 Step 1: Pair of digits of a given number starting with a digit at one's place. Put a horizontal bar to indicate pairing.
 Step 2: Now we need to find a number which on multiplication with itself gives a product of less than or equal to 20. As we know 4 × 4 = 16 < 20. Hence, the divisor is 4 and the quotient is 4.
 Step 3: Now, we have to bring down 00 and multiply the quotient by 2. This give us 8. Hence, 8 is the starting digit of the new divisor.
 Step 4: 4 is placed at one's place of new divisor because when 84 is multiplied by 4 we get 336. The obtained answer now is 64 and we bring down 00.
 Step 5: The quotient now becomes 44 and it is multiplied by 2. This gives 88, which then would become the starting digit of the new divisor.
 Step 6: 7 is placed at one's place of new divisor because on multiplying 887 by 7 we get 6209. This gives the answer 191 and we bring 00 down.
 Step 7: Now the quotient is 447 when multiplied by 2 gives 894, which will be the starting digit of the new divisor.
 Step 8: 2 is the new divisor because on multiplying 8942 by 2 we will get 17884. So, now the answer is 1216 and the next digit of the quotient is 2.
So far we have got √20 = 4.472. On repeating this process further, we get, √20 = 4.4721359549...
Explore Square roots using illustrations and interactive examples
Important Notes:
 20 lies between 16 and 25. So √20 lies between √16 and √25 i.e., √20 lies between 16 and 25
 The prime factorization method is written as a square root of a nonperfect square number in the simplest radical form. For example: 20 = 2 × 2 × 5. So, √20 = √2 × 2 × 5 = 2√5.
Think Tank:
 Is it possible the value of a square root can be negative as well?
 Is √20 a real number?
Square Root of 20 Solved Examples

Example 1: Judy has a squareshaped room having an area of 20 square feet. What will be the length of the room's floor? Round your answer to the nearest tenth.
Solution
Let us assume that the length of the room is x feet. Then the area of the room's floor is x^{2} square feet. By the given information:
x^{2 }= 20
x = √20 = 4.5 feetThe final answer is rounded to the nearest tenth. Hence, the length of the room is 4.5 feet.

Example 2: If the area of a circle is 20π square inches. What is its radius?
Solution
Then area is found using the formula of area of a circle is πr^{2} square inches. By the given information,
πr^{2} = 20π
r^{2} = 20By taking the square root on both sides, √r^{2}= √20. We know that the square root of r^{2} is r.
By calculating the square root of 20 is 4.47 inches. 
Example: If the area of a circle is 20π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 20π in^{2}
⇒ r = ±√20 in
Since radius can't be negative,
⇒ r = √20
The square root of 20 is 4.472.
⇒ r = 4.472 in
FAQs on the Square Root of 20
What is the Value of the Square Root of 20?
The square root of 20 is 4.47213.
Why is the Square Root of 20 an Irrational Number?
Upon prime factorizing 20 i.e. 2^{2} × 5^{1}, 5 is in odd power. Therefore, the square root of 20 is irrational.
What is the Square Root of 20 in Simplest Radical Form?
We need to express 20 as the product of its prime factors i.e. 20 = 2 × 2 × 5. Therefore, √20 = √2 × 2 × 5 = 2 √5. Thus, the square root of 20 in the lowest radical form is 2 √5.
Is the number 20 a Perfect Square?
The prime factorization of 20 = 2^{2} × 5^{1}. Here, the prime factor 5 is not in the pair. Therefore, 20 is not a perfect square.
Evaluate 4 plus 12 square root 20
The given expression is 4 + 12 √20. We know that the square root of 20 is 4.472. Therefore, 4 + 12 √20 = 4 + 12 × 4.472 = 4 + 53.666 = 57.666
What is the Value of 2 square root 20?
The square root of 20 is 4.472. Therefore, 2 √20 = 2 × 4.472 = 8.944.
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