Simplify Square Root of 31302

Here we will show you two methods that you can use to simplify the square root of 31302. In other words, we will show you how to find the square root of 31302 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.

√31302 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 31302 to simplify the square root of 31302. 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 31302. The factors of 31302 are 1, 2, 3, 6, 9, 18, 37, 47, 74, 94, 111, 141, 222, 282, 333, 423, 666, 846, 1739, 3478, 5217, 10434, 15651, and 31302. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 31302 divided by the greatest perfect square from the list of all factors of 31302. We determined above that the greatest perfect square from the list of all factors of 31302 is 9. Furthermore, 31302 divided by 9 is 3478, therefore B equals 3478.

Now we have A and B and can get our answer to 31302 in its simplest radical form as follows:

√31302 = A√B

√31302 = 3√3478

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 31302 to simplify the square root of 31302 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 31302 and then take the square root of that product. The prime factors that multiply together to make 31302 are 2 x 3 x 3 x 37 x 47. 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 31302 by the number (A) squared. 3 squared is 9 and 31302 divided by 9 is 3478. Therefore, B equals 3478.

Once again we have A and B and can get our answer to 31302 in its simplest radical form as follows:

√31302 = A√B

√31302 = 3√3478

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Simplify Square Root of 31303
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