Simplify Square Root of 378

Here we will show you two methods that you can use to simplify the square root of 378. In other words, we will show you how to find the square root of 378 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.

√378 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 378 to simplify the square root of 378. 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 378. The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, and 378. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 378 divided by the greatest perfect square from the list of all factors of 378. We determined above that the greatest perfect square from the list of all factors of 378 is 9. Furthermore, 378 divided by 9 is 42, therefore B equals 42.

Now we have A and B and can get our answer to 378 in its simplest radical form as follows:

√378 = A√B

√378 = 3√42

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 378 to simplify the square root of 378 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 378 and then take the square root of that product. The prime factors that multiply together to make 378 are 2 x 3 x 3 x 3 x 7. 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 378 by the number (A) squared. 3 squared is 9 and 378 divided by 9 is 42. Therefore, B equals 42.

Once again we have A and B and can get our answer to 378 in its simplest radical form as follows:

√378 = A√B

√378 = 3√42

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Simplify Square Root of 379
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