Square root of 19
Did you know Ancient Greeks introduced the idea of square root of positive whole numbers? The square root of 19 is one such number that is irrational. In this chapter, we will calculate the square root of 19 by long division method along with solved examples.
Let us see what the square root of 19 is.
 Square Root of 19: √19 = 4.35889
 Square of 19: 19^{2} = 361
1.  What Is the Square Root of 19? 
2.  Is Square Root of 19 Rational or Irrational? 
3.  Tips and Tricks 
4.  How to Find the Square Root of 19? 
5.  FAQs on Square Root of 19 
6.  Challenging Questions 
What Is the Square Root of 19?
The square root of 19 is the value which is obtained after taking the square root of 19.
Is the Square Root of 19 Rational or Irrational?
It is not possible to find such a whole number which on squaring gives 19. It can be approximately written as a square of 4.359, which is a nonrecurring and nonterminating decimal number. This shows it isn't a perfect square, which also proves that the square root of 19 is an irrational number.
Tips and Tricks:
 19 is not a perfect square, hence its square root is an irrational number. This concludes that the square root of any number "n," which is not a perfect square, will always be an irrational number.
How to Find the Square Root of 19?
The square root of 19 is found using the following steps:
 Step 1: Check whether the number is a perfect square or not.
19 is not a perfect square as it cannot be broken down into a product of two same numbers.
 Step 2: Once the number is checked, the following are the processes required to be followed:
 If the number is a perfect square, it can be written in this format √x^{2} = x.
 If the number is not a perfect square, the square root is found using the long division method. It can also be written in its simplified radical form of the square root.
In this case, 19 is not a perfect square, hence its square root is found using the long division method. The simplified radical form of the square root of 19 is given below.
Simplified Radical Form of Square Root of 34
19 can be written as a product 1 and 19. It is given as:
√19 = √1 × 19
19 is not a perfect square, hence it remains within roots. Simplified radical form of square root of 19 is √19.
Square Root of 34 by Long Division Method
The value of the square root of 19 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
 Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 19. So, the number is 4. Putting the divisor as 4, we get the quotient as 4 and the remainder as 3.
 Step 3: Double the quotient and enter it with a blank on its right. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places you want.
Hence, √19 = 4.358
Explore square roots using illustrations and interactive examples.
Challenging Questions:
 How will Hailey find the square root of 19 using the long division method up to 6 decimal places?
 How will Billy express the square root of 57 in terms of square root of 19?
Square Root of 19 Solved Examples

Example 1: Can you find the two consecutive numbers between which the square root of 19 lies?
Solution
The perfect squares nearest to 19 are 16 and 25. The square root of 16 is given as 4. The square root of 25 is given as 5.
Thus, 4 and 5 are the two numbers between which the square root of 19 lies. 
Example 2: Is the square root of 38 double the square root of 19?
Solution
38 can be expressed as √38 =√2 × 19. Taking half of square root of 38 he will get,
√38/2 = (√2 × 19)/2 = √19/√2 = √19/2
The square root of 19 is √19. Hence, the square root of 38 is not the double of the square root of 19.
FAQs on Square Root of 19
What is the square root of 19?
The square root of 19 is approximately 4.36.
Is the square root of 19 in its simplest form?
Yes, the square root of 19 is already in its simplest form.
What is the square root of 19 simplified?
19 is not a perfect square. Thus, its square root cannot be simplified further.
How do you find the square root of a number?
Square roots are found out by the following steps:
 Step 1: Check whether the number is a perfect square or not.
 Step 2: Once the number is checked, the following are the processes required to be followed:
 If the number is a perfect square, it can be written in this format √x^{2} = x.
 If the number is a perfect square, the square root is given as x. Otherwise, it can also be written in its simplified radical form of the square root.
Is square root of 19 a rational or irrational number?
The square root of 19 is an irrational number.
Is square root of 19 a real number?
Yes, the square root of 19 is a real number.