Simplify Square Root of 1000

Here we will show you step-by-step how to simplify the square root of 1000. The square root of 1000 can be written as follows:


	√	1000

The √ symbol is called the radical sign. To simplify the square root of 1000 means to get the simplest radical form of √1000.

Step 1: List Factors
List the factors of 1000 like so:

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

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

1, 4, 25, 100

Step 3: Divide
Divide 1000 by the largest perfect square you found in the previous step:

1000 / 100 = 10

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

√100 = 10

Step 5: Get Answer
Put Steps 3 and 4 together to get the square root of 1000 in its simplest form:


10	√	10

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Decimal Form
Square Root of 1000 in Decimal form rounded to nearest 5 decimals:

31.62278

Exponent Form
Square Root of 1000 written with Exponent instead of Radical:

1000^½ = 10 x 10^½

Simplify Square Root of 1001
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* List of Perfect Squares