Simplify Square Root of 72501

Here we will show you two methods that you can use to simplify the square root of 72501. In other words, we will show you how to find the square root of 72501 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.

√72501 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72501 to simplify the square root of 72501. 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 72501. The factors of 72501 are 1, 3, 11, 13, 33, 39, 143, 169, 429, 507, 1859, 2197, 5577, 6591, 24167, and 72501. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 72501 divided by the greatest perfect square from the list of all factors of 72501. We determined above that the greatest perfect square from the list of all factors of 72501 is 169. Furthermore, 72501 divided by 169 is 429, therefore B equals 429.

Now we have A and B and can get our answer to 72501 in its simplest radical form as follows:

√72501 = A√B

√72501 = 13√429

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72501 to simplify the square root of 72501 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 72501 and then take the square root of that product. The prime factors that multiply together to make 72501 are 3 x 11 x 13 x 13 x 13. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 72501 by the number (A) squared. 13 squared is 169 and 72501 divided by 169 is 429. Therefore, B equals 429.

Once again we have A and B and can get our answer to 72501 in its simplest radical form as follows:

√72501 = A√B

√72501 = 13√429

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Simplify Square Root of 72502
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