Square Root of 20

Square Root of 20 is equal to 4.47213595. It is represented as √20 or 20^1/2. Square Root of a number is the number that when multiplied by itself gives the original number which is called the Square of the Square Root number.

In this article, we will learn what is the value of the square root of 20, how to find the value of the square root of 20.

What is Square Root of 20?

Value of the Square Root of 20 is often called the value of root 20 which is given as follows:

Square Root of 20 = √20 = 4.47213595

In square root form, the value of the square root of 20 is given as √20 = 2√5. Since the decimal value of √5 is 2.236, the root of 20 can also be written in the decimal form as 4.4721. The extended square root of 20 is 4.47213595.

In standard cases, the square root of a number is calculated only up to three digits after decimal.

How to Find the Square Root of 20?

As mentioned, the square root of a number is a whole number that when multiplied with itself, gives the original number.

We can find the square root of 20 using following two methods:

• Square Root 20 Value by Long Division Method
• Square Root of 20 Using Prime Factorization

Let’s learn, these methods in detail.

Square Root 20 Value by Long Division Method

In the case of 20, since 20 is not a perfect square, we will have to use the long division method to find its square root. Long Division Method is the most suitable method to find the value of square root of non perfect square numbers. Follow the following steps to find the square root of 20 using the long division method:

Step 1: Write 20 as 20.000000. We will be using these zeroes for decimal division later on.

Step 2: Search for the perfect square that is less than 20. In this case, it is 16.

Step 3: To obtain, 16 we will use 4 as divisor, hence, the quotient at this point is 4 and the remainder is 4.

Step 4: Put a decimal in the quotient and bring one pair of zeroes next to the remainder 4. and add 4 in the divisor

Step 5: Now we have 8 as new divisor and 400 as new dividend

Step 6: Now find a number for the unit place of divisor such that the same number can be placed in the quotient after the decimal and the resultant product of the divisor and the new number in quotient is smaller than or equal to the dividend. In this case, that number is 4 since 84 × 4 = 336 which is less than 400.

Step 6: Bring the next pair of zeroes down and repeat steps 4 and 5.

You can calculate these values upto two decimal places to get an approximate value for the square root of 20.

Learn, Square Root by Long Division Method

Square Root of 20 using Prime Factorization

When expressed as a product of its primes, 20 can be written as: 2 × 2 × 5

Hence, √20 = √(2 × 2 × 5)

When we calculate the square root of a perfect square number, we simply take one value out of the two repeated ones and multiply them to get an answer.

However, in the case of 20, we can pick 2 out of 2 × 2 as (2 × 2)^1/2 = (2²)^1/2 = 2, but since 5 does not have a pair, we cannot do the same with 5 and hence 5 will remain under the square root

Hence, the value of square root using prime factorization is given as:

√20 = 2 × √5 or 2√5

Square Root of 20 – FAQs

What is Value of Root 20?

The value of square root of 20 in decimal form is equal to 4.47213595….

Is Square root of 20 Rational or Irrational?

Since, the square root of 20 is 4.47213595…. We can see that it is neither terminating nor non-terminating repeating. Thus, the square root of 20 is an irrational number.

How to Write Square Root of 20?

Square Root of 20 can be written as √20.

Is 20 a Perfect Square?

No, 20 is not a perfect square because it’s prime factors 2 x 2 x 5 can’t be paired because of a single value of 5.

Is -2√5 a Square Root of 20?

Yes, -2√5 is a square root of 20 as, (-2√5) × (-2√5) = 4 × 5 = 20

What is the Square of √20?

The square of √20 = (√20)2 = (20^1/2)² is equal to 20