Simplify Square Root of 363

Here we will show you two methods that you can use to simplify the square root of 363. In other words, we will show you how to find the square root of 363 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.

√363 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 363 to simplify the square root of 363. 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 363. The factors of 363 are 1, 3, 11, 33, 121, and 363. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 363 divided by the greatest perfect square from the list of all factors of 363. We determined above that the greatest perfect square from the list of all factors of 363 is 121. Furthermore, 363 divided by 121 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 363 in its simplest radical form as follows:

√363 = A√B

√363 = 11√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 363 to simplify the square root of 363 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 363 and then take the square root of that product. The prime factors that multiply together to make 363 are 3 x 11 x 11. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 363 by the number (A) squared. 11 squared is 121 and 363 divided by 121 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 363 in its simplest radical form as follows:

√363 = A√B

√363 = 11√3

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Simplify Square Root of 364
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