Simplify Square Root of 63654

Here we will show you two methods that you can use to simplify the square root of 63654. In other words, we will show you how to find the square root of 63654 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.

√63654 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63654 to simplify the square root of 63654. 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 63654. The factors of 63654 are 1, 2, 3, 6, 103, 206, 309, 618, 10609, 21218, 31827, and 63654. Furthermore, the greatest perfect square on this list is 10609 and the square root of 10609 is 103. Therefore, A equals 103.

B = Calculate 63654 divided by the greatest perfect square from the list of all factors of 63654. We determined above that the greatest perfect square from the list of all factors of 63654 is 10609. Furthermore, 63654 divided by 10609 is 6, therefore B equals 6.

Now we have A and B and can get our answer to 63654 in its simplest radical form as follows:

√63654 = A√B

√63654 = 103√6

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63654 to simplify the square root of 63654 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 63654 and then take the square root of that product. The prime factors that multiply together to make 63654 are 2 x 3 x 103 x 103. When we strip out the pairs only, we get 103 x 103 = 10609 and the square root of 10609 is 103. Therefore, A equals 103.

B = Divide 63654 by the number (A) squared. 103 squared is 10609 and 63654 divided by 10609 is 6. Therefore, B equals 6.

Once again we have A and B and can get our answer to 63654 in its simplest radical form as follows:

√63654 = A√B

√63654 = 103√6

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Simplify Square Root of 63655
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