Simplify Square Root of 31308

Here we will show you two methods that you can use to simplify the square root of 31308. In other words, we will show you how to find the square root of 31308 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.

√31308 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 31308 to simplify the square root of 31308. 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 31308. The factors of 31308 are 1, 2, 3, 4, 6, 12, 2609, 5218, 7827, 10436, 15654, and 31308. Furthermore, the greatest perfect square on this list is 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Calculate 31308 divided by the greatest perfect square from the list of all factors of 31308. We determined above that the greatest perfect square from the list of all factors of 31308 is 4. Furthermore, 31308 divided by 4 is 7827, therefore B equals 7827.

Now we have A and B and can get our answer to 31308 in its simplest radical form as follows:

√31308 = A√B

√31308 = 2√7827

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 31308 to simplify the square root of 31308 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 31308 and then take the square root of that product. The prime factors that multiply together to make 31308 are 2 x 2 x 3 x 2609. When we strip out the pairs only, we get 2 x 2 = 4 and the square root of 4 is 2. Therefore, A equals 2.

B = Divide 31308 by the number (A) squared. 2 squared is 4 and 31308 divided by 4 is 7827. Therefore, B equals 7827.

Once again we have A and B and can get our answer to 31308 in its simplest radical form as follows:

√31308 = A√B

√31308 = 2√7827

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Simplify Square Root of 31309
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