Simplify Square Root of 75

Here we will show you step-by-step how to simplify the square root of 75. The square root of 75 can be written as follows:


	√	75

The √ symbol is called the radical sign. To simplify the square root of 75 means to get the simplest radical form of √75.

Step 1: List Factors
List the factors of 75 like so:

1, 3, 5, 15, 25, 75

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

1, 25

Step 3: Divide
Divide 75 by the largest perfect square you found in the previous step:

75 / 25 = 3

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

√25 = 5

Step 5: Get Answer
Put Steps 3 and 4 together to get the square root of 75 in its simplest form:


5	√	3

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Decimal Form
Square Root of 75 in Decimal form rounded to nearest 5 decimals:

8.66025

Exponent Form
Square Root of 75 written with Exponent instead of Radical:

75^½ = 5 x 3^½

Simplify Square Root of 76
The answer to Simplify Square Root of 75 is not the only problem we solved. Go here for the next problem on our list.

* List of Perfect Squares