Simplify Square Root of 312

Here we will show you step-by-step how to simplify the square root of 312. The square root of 312 can be written as follows:


	√	312

The √ symbol is called the radical sign. To simplify the square root of 312 means to get the simplest radical form of √312.

Step 1: List Factors
List the factors of 312 like so:

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

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

1, 4

Step 3: Divide
Divide 312 by the largest perfect square you found in the previous step:

312 / 4 = 78

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

√4 = 2

Step 5: Get Answer
Put Steps 3 and 4 together to get the square root of 312 in its simplest form:


2	√	78

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Decimal Form
Square Root of 312 in Decimal form rounded to nearest 5 decimals:

17.66352

Exponent Form
Square Root of 312 written with Exponent instead of Radical:

312^½ = 2 x 78^½

Simplify Square Root of 313
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* List of Perfect Squares