Simplify Square Root of 372

Here we will show you two methods that you can use to simplify the square root of 372. In other words, we will show you how to find the square root of 372 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.

√372 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 372 to simplify the square root of 372. 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 372. The factors of 372 are 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, and 372. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 372 divided by the greatest perfect square from the list of all factors of 372. We determined above that the greatest perfect square from the list of all factors of 372 is 4. Furthermore, 372 divided by 4 is 93, therefore B equals 93.

Now we have A and B and can get our answer to 372 in its simplest radical form as follows:

√372 = A√B

√372 = 2√93

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 372 to simplify the square root of 372 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 372 and then take the square root of that product. The prime factors that multiply together to make 372 are 2 x 2 x 3 x 31. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 372 by the number (A) squared. 2 squared is 4 and 372 divided by 4 is 93. Therefore, B equals 93.

Once again we have A and B and can get our answer to 372 in its simplest radical form as follows:

√372 = A√B

√372 = 2√93

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Simplify Square Root of 373
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