Simplify Square Root of 7728

Here we will show you step-by-step how to simplify the square root of 7728. The square root of 7728 can be written as follows:


	√	7728

The √ symbol is called the radical sign. To simplify the square root of 7728 means to get the simplest radical form of √7728.

Step 1: List Factors
List the factors of 7728 like so:

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864, 7728

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

1, 4, 16

Step 3: Divide
Divide 7728 by the largest perfect square you found in the previous step:

7728 / 16 = 483

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

√16 = 4

Step 5: Get Answer
Put Steps 3 and 4 together to get the square root of 7728 in its simplest form:


4	√	483

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Decimal Form
Square Root of 7728 in Decimal form rounded to nearest 5 decimals:

87.90904

Exponent Form
Square Root of 7728 written with Exponent instead of Radical:

7728^½ = 4 x 483^½

Simplify Square Root of 7729
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* List of Perfect Squares