Simplify Square Root of 25947

Here we will show you two methods that you can use to simplify the square root of 25947. In other words, we will show you how to find the square root of 25947 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.

√25947 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 25947 to simplify the square root of 25947. 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 25947. The factors of 25947 are 1, 3, 9, 27, 31, 93, 279, 837, 961, 2883, 8649, and 25947. Furthermore, the greatest perfect square on this list is 8649 and the square root of 8649 is 93. Therefore, A equals 93.

B = Calculate 25947 divided by the greatest perfect square from the list of all factors of 25947. We determined above that the greatest perfect square from the list of all factors of 25947 is 8649. Furthermore, 25947 divided by 8649 is 3, therefore B equals 3.

Now we have A and B and can get our answer to 25947 in its simplest radical form as follows:

√25947 = A√B

√25947 = 93√3

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 25947 to simplify the square root of 25947 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 25947 and then take the square root of that product. The prime factors that multiply together to make 25947 are 3 x 3 x 3 x 31 x 31. When we strip out the pairs only, we get 3 x 3 x 31 x 31 = 8649 and the square root of 8649 is 93. Therefore, A equals 93.

B = Divide 25947 by the number (A) squared. 93 squared is 8649 and 25947 divided by 8649 is 3. Therefore, B equals 3.

Once again we have A and B and can get our answer to 25947 in its simplest radical form as follows:

√25947 = A√B

√25947 = 93√3

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Simplify Square Root of 25948
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