The square root of 19 is expressed as √19 in the radical form and as (19)½ or (19)0.5 in the exponent form. The square root of 19 rounded up to 9 decimal places is 4.358898944. It is the positive solution of the equation x2 = 19.

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Square Root of 19: 4.358898943540674Square Root of 19 in exponential form: (19)½ or (19)0.5Square Root of 19 in radical form: √19
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 non-recurring and non-terminating 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 x2 = 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.

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Hence, 19 = 4.358

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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?