Did you know that 192 is the amount of ten consecutive primes? In this lesson, we will certainly calculate the square source of 192 by long division method. Us will additionally go v a few solved examples and interactive questions related come the square root of 192.

You are watching: Square root of 192 in radical form

Square source of 192192 = 13.8564Square the 192: 1922 = 36,864
1.What Is the Square root of 192?
2.Is Square root of 192 rational or Irrational?
3.Tips and also Tricks
4.How to discover the Square root of 192?
5.FAQs top top Square root of 192
6.Challenging Questions

The square root of 192 is the value which once multiplied by chin will offer the last product as 192.


It is not possible to uncover a whole number which ~ above squaring gives 192. It can be around written as a square that 13.856, i beg your pardon is a non-recurring and also non-terminating decimal number. This indicates that 192 is not a perfect square which also proves that the square root of 192 is one irrational number.

Tips and also Tricks:

192 is not a perfect square; hence, the square source is one irrational number. The square source of any number n, i beg your pardon is no a perfect square, will always be an irrational number.

How to uncover the Square root of 192?

The square root of 192 deserve to be discovered using the adhering to steps:

Step 1: check whether the number is a perfect square or not. 192 is no a perfect square as it cannot be broken down into a product that two same numbers.Step 2: as soon as the number is checked, we have the right to do the following:A number which is a perfect square can be created as x2 = x.For a number i m sorry is not a perfect square, the square root deserve to be found using the long division method. This number can likewise be composed in its streamlined radical kind of the square root.

In this case, 192 is not a perfect square. Hence, the square source is uncovered using the long department method. The simplified radical form of the square root of 192 is offered below.

Simplified Radical kind of Square root of 192

192 can be written as the product of 3 and 64. It is provided as:

192 = 3 × 64

3 is no a perfect square. Hence, it stays within the root sign. However, 64 have the right to be displayed as 82. Thus, the simplified radical form of the square source of 192 is 83.

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Square source of 192 by Long division Method

The square source of 192 can be discovered using the long division method. These space the measures to it is in followed: 

Step 1: starting from the right, we will pair up the number by placing a bar over them.Step 2: Find a number together that once you main point it through itself, the product is less than or same to 192. Maintaining the divisor as 23, we obtain the quotient together 13 and the remainder 92-69 = 23. Step 3: double the divisor and enter it with a empty on the right. Climate assume the biggest digit to replace the empty - this will end up being the new digit in the quotient. Now, as soon as the new divisor will be multiplied to the brand-new quotient, the final product will be lesser 보다 or equal to our dividend. Finally, divide and write the remainder. Guess the largest feasible digit to to fill the empty which will also become the new digit in the quotient, together that once the new divisor is multiply to the new quotient the product is less than or same to the dividend. Divide and write the remainder. Repeat this process to get the decimal locations you want. 

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Hence, √192 = 13.856

Explore square roots using illustrations and interactive examples

Challenging Questions:

How will Hailey discover the square root of 192 using the long department method up to 5 decimal places?How will certainly Mandy express the square source of 384 in terms of square root of 192?