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Square Root

What Is the Square Root of 20? | Find the Square Root of 20

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 20? | Find the Square Root of 20

What Is the Square Root of 20? | Find the Square Root of 20

The square root of 20 is 4.4721. The inversion operation of addition is subtraction; the same goes for multiplication and division. Understanding a square root is as simple as that. The inversion of the square root value is squaring the given number.

The square root of the number is the value when multiplied by itself gives the original number. For the number that are perfectly square, there are three ways to find them for the numbers that are not square use of the long division is the standard way to find them.

When a number is given for which a square root has to be found. First, we have to check whether the number is a perfect square or not or you can also check if the number is an irrational number or not. To know whether the number is rational or irrational.

Let us take two numbers p and q if p,q  ≠0 then the number is a rational number. If the two numbers p and q when divided equally to 0 then the given number is an irrational number p,q  ≠0.

Methods to find the square root of 20

There are three methods to find the square root of a number

  • Prime factorization method
  • Long division method

Prime factorization

The prime factors of 20 = 225
20 = 22 ×5
= 2×√5
= 2 ×2.236
= 4.4721

Long division method

  • Step 1: Find the nearest integer that can divide the number
    • The nearest integer that can divide 20 is 4. 
  • Step 2: Divide the numbers until you reach a satisfactory digit after the decimal
Long division method
Long division method
  • Step 3: The quotient is the square root of the number
    • √20 = 4.472

Solved examples

Q1: Find the square root of 36 using the repeated subtraction method

A 1:
36-1 = 35
35-3 = 32
32-5 = 27
27-7 = 20
20-9 = 11
11-11 = 0

√36 = 6

Q2: What is the square root of 20

Long division method

A2: √20 = 4.472

Q3: Luke is playing in his yard. The gate in his yard is 12 square feet. Find the height of the gate. 
A3: If we find the square root area of the gate then we can easily find the height of the gate,
Use the knowledge of square root to find the solution,
12 = √ 3 ×√ 4
√12 = √ 3× 2 =  2√ 3
The side length of the gate = 2√ 3 feet

Q4: What is the square root of 144
A4: √144 = 12×12
The square root of √144 = 12

Q5: What is the square root of 3

Long division method
Long division method

A5: √3 = 1.732

Frequently asked questions

Which is the standard method to find the square root of an irrational number
The standard method to find the square root of an irrational number is the long division method.

What is the square root of 20
The √20 = 4.472

How to write the square root of 20 in exponential form? 
201/2 or 200.5 is the exponential way to write √20

How to write the square root of 20 in radical form?
The radical form of writing square root is √20

Can I find the square root of 20 using other methods?
Finding the square root for 20 is possible using the prime factorization and the long division method.

Is 20  an irrational number?
Yes, 20 is an irrational number since the number is not equal to zero

What are the methods to find the square root of a number?
There are three methods to find the square root of a number
Prime factorization method
Long division method
Repeated subtraction

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Prerit Jain

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