Simplify Square Root of 72250

Here we will show you two methods that you can use to simplify the square root of 72250. In other words, we will show you how to find the square root of 72250 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.

√72250 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 72250 to simplify the square root of 72250. 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 72250. The factors of 72250 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 125, 170, 250, 289, 425, 578, 850, 1445, 2125, 2890, 4250, 7225, 14450, 36125, and 72250. Furthermore, the greatest perfect square on this list is 7225 and the square root of 7225 is 85. Therefore, A equals 85.

B = Calculate 72250 divided by the greatest perfect square from the list of all factors of 72250. We determined above that the greatest perfect square from the list of all factors of 72250 is 7225. Furthermore, 72250 divided by 7225 is 10, therefore B equals 10.

Now we have A and B and can get our answer to 72250 in its simplest radical form as follows:

√72250 = A√B

√72250 = 85√10

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 72250 to simplify the square root of 72250 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 72250 and then take the square root of that product. The prime factors that multiply together to make 72250 are 2 x 5 x 5 x 5 x 17 x 17. When we strip out the pairs only, we get 5 x 5 x 17 x 17 = 7225 and the square root of 7225 is 85. Therefore, A equals 85.

B = Divide 72250 by the number (A) squared. 85 squared is 7225 and 72250 divided by 7225 is 10. Therefore, B equals 10.

Once again we have A and B and can get our answer to 72250 in its simplest radical form as follows:

√72250 = A√B

√72250 = 85√10

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Simplify Square Root of 72251
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