Simplify Square Root of 63283

Here we will show you two methods that you can use to simplify the square root of 63283. In other words, we will show you how to find the square root of 63283 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.

√63283 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63283 to simplify the square root of 63283. 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 63283. The factors of 63283 are 1, 11, 121, 523, 5753, and 63283. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 63283 divided by the greatest perfect square from the list of all factors of 63283. We determined above that the greatest perfect square from the list of all factors of 63283 is 121. Furthermore, 63283 divided by 121 is 523, therefore B equals 523.

Now we have A and B and can get our answer to 63283 in its simplest radical form as follows:

√63283 = A√B

√63283 = 11√523

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63283 to simplify the square root of 63283 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 63283 and then take the square root of that product. The prime factors that multiply together to make 63283 are 11 x 11 x 523. 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 63283 by the number (A) squared. 11 squared is 121 and 63283 divided by 121 is 523. Therefore, B equals 523.

Once again we have A and B and can get our answer to 63283 in its simplest radical form as follows:

√63283 = A√B

√63283 = 11√523

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Simplify Square Root of 63284
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