Simplify Square Root of 387

Here we will show you two methods that you can use to simplify the square root of 387. In other words, we will show you how to find the square root of 387 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.

√387 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 387 to simplify the square root of 387. 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 387. The factors of 387 are 1, 3, 9, 43, 129, and 387. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 387 divided by the greatest perfect square from the list of all factors of 387. We determined above that the greatest perfect square from the list of all factors of 387 is 9. Furthermore, 387 divided by 9 is 43, therefore B equals 43.

Now we have A and B and can get our answer to 387 in its simplest radical form as follows:

√387 = A√B

√387 = 3√43

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 387 to simplify the square root of 387 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 387 and then take the square root of that product. The prime factors that multiply together to make 387 are 3 x 3 x 43. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 387 by the number (A) squared. 3 squared is 9 and 387 divided by 9 is 43. Therefore, B equals 43.

Once again we have A and B and can get our answer to 387 in its simplest radical form as follows:

√387 = A√B

√387 = 3√43

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Simplify Square Root of 388
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