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 x² = 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

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.

A rational number is either terminating or non-terminating and has a repeating pattern in its decimal part. We saw that √20 = 4.4721359549. This is non-terminating and the decimal part has no repeating pattern. So it is NOT a rational number. Hence, √20 is an irrational number.

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

• Square Root of 22
• Square Root of 26
• Square Root of 27
• Square Root of 28
• Square Root of 29

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 non-perfect 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?