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
| 1. | What Is the Square Root of 20? |
| 2. | IsSquare 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 rootof 20 can be obtained by thenumber whose square gives the original number. What number that could be? Itcan be seen that, there are nointegers whose square will give20.
√20= 4.472
To check this answer, we can find (4.472)2and we can see that we get thenumber 19.998784 ... which is very close to 20 when it's rounded to its nearest value.
Is the Square Root of 20Rational orIrrational?
A rational number is either terminating or non-terminating and has a repeatingpattern 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,√20is an irrational number.
How to Find the Square Root of 20?
There are differentmethods to find the square root of any number. Click hereto know more about it.
Simplified Radical Form of Square Root of 20
20 is not a prime number. Thus it has morethan twofactors, 1, 2, 4, 5, 10and 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 20is 2× 2× 5which has 1pairof the same number. Thus, the simplest radical form of √20is 2√5itself.
Square Root of 20by Long Division Method
The square root of 20can 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 horizontalbar to indicatepairing.
- Step 2:Now we need to find a number which on multiplicationwithitself gives a product of less than or equal to 20. As we know 4× 4= 16 < 20. Hence,the divisor is 4and the quotient is 4.
- Step 3:Now, we have to bring down 00 and multiply the quotient by 2. Thisgive us 8. Hence, 8is the starting digit of thenew divisor.
- Step 4: 4isplaced atone's place of new divisor because when 84is multiplied by 4we get 336. The obtained answer now is 64 and we bring down 00.
- Step 5: The quotient now becomes 44 and itis multiplied by 2. Thisgives 88, which then would become the starting digit of the new divisor.
- Step 6: 7is placed at one's place of new divisor because on multiplying 887by 7we get 6209. This gives the answer 191 and we bring 00 down.
- Step 7: Now the quotient is447when multiplied by2 gives 894, which will bethe starting digit of the new divisor.
- Step 8: 2is the new divisor because on multiplying 8942by 2we will get 17884. So, now the answer is 1216and 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 16and 25. So √20 lies between √16and√25i.e., √20lies between 16and 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 canbe negative as well?
- Is √-20a real number?
Square Root of 20 Solved Examples
Example 1: Judyhas a square-shaped room havingan area of 20square feet. What will bethe length of the room's floor? Round your answer to the nearest tenth.
Solution
Let us assume that the length of the room is xfeet. Then the area of the room's floor is x2square feet. By the given information:
x2= 20
x = √20= 4.5feetThe final answer is rounded to the nearest tenth. Hence, the length of the room is 4.5feet.
Example 2: If the area of a circle is 20πsquare inches. What is its radius?
Solution
Then area is foundusing the formula of area of a circle is πr2square inches. By the given information,
πr2= 20π
r2 = 20By taking the square root on both sides, √r2=√20.We know that the square root of r2 is r.
By calculating the square root of 20is 4.47inches.Example: If the area of a circle is 20π in2. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr2 = 20π in2
⇒ r = ±√20 in
Since radius can't be negative,
⇒ r = √20
The square root of 20 is 4.472.
⇒ r = 4.472 in
Show Answer >
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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. 22 × 51, 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 = 22 × 51. 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.
