Simplify Square Root of 192

Here we will show you step-by-step how to simplify the square root of 192. The square root of 192 can be written as follows:


	√	192

The √ symbol is called the radical sign. To simplify the square root of 192 means to get the simplest radical form of √192.

Step 1: List Factors
List the factors of 192 like so:

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192

Step 2: Find Perfect Squares
Identify the perfect squares* from the list of factors above:

1, 4, 16, 64

Step 3: Divide
Divide 192 by the largest perfect square you found in the previous step:

192 / 64 = 3

Step 4: Calculate
Calculate the square root of the largest perfect square:

√64 = 8

Step 5: Get Answer
Put Steps 3 and 4 together to get the square root of 192 in its simplest form:


8	√	3

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Decimal Form
Square Root of 192 in Decimal form rounded to nearest 5 decimals:

13.85641

Exponent Form
Square Root of 192 written with Exponent instead of Radical:

192^½ = 8 x 3^½

Simplify Square Root of 193
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* List of Perfect Squares