What is square root of 20

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The number 20 is an even number that has 6 factors, such as 1, 2, 4, 5, 10 and 20. Square root of 20 is expressed as √20. This is called a radical form of mathematical representation. Some children might find it easy and quite a few might find it difficult to understand the numbers, their square root and the squares. Hence, parents and teachers can help them learn the square root of 20 by teaching them 20 Times Table, available at Osmo. Kids learn fast when fun, educational and interactive games are a part of their learning process. Make it more convenient for kids so that they grasp the concept of square root in a fun way

What is the Square Root of 20?

The square root of 20 is 4.472. When the number 4.472 is multiplied by 4.472, the product obtained is 20. However, this is a non terminating number. The actual number obtained when multiplying 4.472 is = 4.472 x 4.472 = 19.998. Hence, 19.998 is rounded to its closest number which is 20. In addition, one of the best practices to teach the little learners this concept is to introduce them to Multiplication Worksheets, available at Osmo. The square root of 20 is represented in 3 ways such as,

• Radical form: √20
• Decimal form: 4.47213
• (20)½ or (20)0.5

How to Find the Square Root of 20?

The square root of 20 can be found in many ways. Easiest of all is the simplified radical form and the long division method.

Simplified Radical form

As mentioned above, 20 is an even number and not a prime number with six factors, 1, 2, 4, 5, 10 and 20. To determine the square root of 20, you must take one numeral from each set of similar digits from its prime factorization and multiply. That is mathematically expressed as,

20 = 2 x 2 x 5 (one set of same numerals)

Therefore, the simplified radical form of the square root of 20 or √20 is 2√5.

How to Find the Square Root of Negative 20?

The square root of 20 is 4.4721359. But, the square root of -20 is a complex and an imaginary digit. Now, let us learn and understand how to determine the square root of negative 20.

• The mathematical representation of negative 20 = √20 x √-1
• The square root of 20 is written in the radical form as √20. √20 = 4.472, and √-1 is represented as an i
• Finally, the square root of negative 20 is equal to 4.472i

Is the Square Root of 20 Rational or Irrational?

A rational number implies non terminating or termination numerals that have repeated patterns in the decimal places. In this case, √20 = 4.472. This is a non terminating number without repetitive patterns. Thus, it is not a rational number and √20 is an irrational number.

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Yes. √-20 is an imaginary number.

Yes. √20 can be expressed in decimal form.

The value of the square root of 20 is 4.472135955 and is denoted as √20 in radical form. This value we can easily get from the calculator. But, students should know how to simplify the root of any number without using a calculator. This is possible by using two methods: Prime factorisation and long division method. Both methods are very simple and are easy ways to find the square root.

Square root of 20, √20 = 4.4721 (in round figures)

The square root of 20 is represented as √20, where √ is the radical sign and 20 is said to be radicand. In the simplest form, the √20 can be written as 2√5. Therefore, here we cannot say that √20 is a rational number since √5 is an irrational number.

Now, let us learn here to find the value of √20.

Simplification of Square Root of 20

The simple method to find the value of √20 is to factorise the number under the root, i.e. 20.

The prime factorisation of 20 gives:

20 = 2 x 2 x 5 = 22 x 5

Thus, here we can see, 20 is not a perfect square, because we cannot pair digit 5 after factoring 20. Only 22 can be taken out of the root.

Hence, if we take the roots on both sides, we get;

√20 = √(2 x 2 x 5)

Here, we just have only one pair of numbers, which is 2. Therefore, taking it outside the root, we get;

√20 = 2√5

From the square root table, we know the value of √5 = 2.236

Hence,

√20 = 2 x 2.236

√20 = 4.472

Using Long Division Method

We have learned to calculate the value of the square root of 20 using prime factorisation. But it is not a direct method to find the value because 20 is an imperfect square and we need to remember the √5 value to find the accurate value of √20.

By using long division method, we can use the accurate value of √20. Below is the solved step presented to evaluate √20.

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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...

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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? 

1. Example 1: Judy has a square-shaped 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 x2 square feet. By the given information:

   x2 = 20
   x = √20 = 4.5 feet

   The final answer is rounded to the nearest tenth. Hence, the length of the room is 4.5 feet.

2. 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 πr2 square inches. By the given information,

   πr2 = 20π 
   r2 = 20

   By 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 20 is 4.47 inches.

3. 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

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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.