Simplify Square Root of 75

Here we will show you two methods that you can use to simplify the square root of 75. In other words, we will show you how to find the square root of 75 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√75 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 75 to simplify the square root of 75. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 75. The factors of 75 are 1, 3, 5, 15, 25, and 75. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 75 divided by the greatest perfect square from the list of all factors of 75. We determined above that the greatest perfect square from the list of all factors of 75 is 25. Furthermore, 75 divided by 25 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 75 in its simplest radical form as follows:

√75 = A√B

√75 = 5√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 75 to simplify the square root of 75 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 75 and then take the square root of that product. The prime factors that multiply together to make 75 are 3 x 5 x 5. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 75 by the number (A) squared. 5 squared is 25 and 75 divided by 25 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 75 in its simplest radical form as follows:

√75 = A√B

√75 = 5√3

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Simplify Square Root of 76
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