Simplify Square Root of 31257

Here we will show you two methods that you can use to simplify the square root of 31257. In other words, we will show you how to find the square root of 31257 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.

√31257 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 31257 to simplify the square root of 31257. 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 31257. The factors of 31257 are 1, 3, 9, 23, 69, 151, 207, 453, 1359, 3473, 10419, and 31257. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 31257 divided by the greatest perfect square from the list of all factors of 31257. We determined above that the greatest perfect square from the list of all factors of 31257 is 9. Furthermore, 31257 divided by 9 is 3473, therefore B equals 3473.

Now we have A and B and can get our answer to 31257 in its simplest radical form as follows:

√31257 = A√B

√31257 = 3√3473

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 31257 to simplify the square root of 31257 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 31257 and then take the square root of that product. The prime factors that multiply together to make 31257 are 3 x 3 x 23 x 151. 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 31257 by the number (A) squared. 3 squared is 9 and 31257 divided by 9 is 3473. Therefore, B equals 3473.

Once again we have A and B and can get our answer to 31257 in its simplest radical form as follows:

√31257 = A√B

√31257 = 3√3473

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Simplify Square Root of 31258
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