Simplify Square Root of 25506

Here we will show you two methods that you can use to simplify the square root of 25506. In other words, we will show you how to find the square root of 25506 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.

√25506 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25506 to simplify the square root of 25506. 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 25506. The factors of 25506 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 109, 117, 218, 234, 327, 654, 981, 1417, 1962, 2834, 4251, 8502, 12753, and 25506. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 25506 divided by the greatest perfect square from the list of all factors of 25506. We determined above that the greatest perfect square from the list of all factors of 25506 is 9. Furthermore, 25506 divided by 9 is 2834, therefore B equals 2834.

Now we have A and B and can get our answer to 25506 in its simplest radical form as follows:

√25506 = A√B

√25506 = 3√2834

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25506 to simplify the square root of 25506 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 25506 and then take the square root of that product. The prime factors that multiply together to make 25506 are 2 x 3 x 3 x 13 x 109. 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 25506 by the number (A) squared. 3 squared is 9 and 25506 divided by 9 is 2834. Therefore, B equals 2834.

Once again we have A and B and can get our answer to 25506 in its simplest radical form as follows:

√25506 = A√B

√25506 = 3√2834

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Simplify Square Root of 25507
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