Simplify Square Root of 72702

Here we will show you two methods that you can use to simplify the square root of 72702. In other words, we will show you how to find the square root of 72702 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.

√72702 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72702 to simplify the square root of 72702. 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 72702. The factors of 72702 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 577, 1154, 1731, 3462, 4039, 5193, 8078, 10386, 12117, 24234, 36351, and 72702. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 72702 divided by the greatest perfect square from the list of all factors of 72702. We determined above that the greatest perfect square from the list of all factors of 72702 is 9. Furthermore, 72702 divided by 9 is 8078, therefore B equals 8078.

Now we have A and B and can get our answer to 72702 in its simplest radical form as follows:

√72702 = A√B

√72702 = 3√8078

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72702 to simplify the square root of 72702 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 72702 and then take the square root of that product. The prime factors that multiply together to make 72702 are 2 x 3 x 3 x 7 x 577. 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 72702 by the number (A) squared. 3 squared is 9 and 72702 divided by 9 is 8078. Therefore, B equals 8078.

Once again we have A and B and can get our answer to 72702 in its simplest radical form as follows:

√72702 = A√B

√72702 = 3√8078

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Simplify Square Root of 72703
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