Simplify Square Root of 81275

Here we will show you two methods that you can use to simplify the square root of 81275. In other words, we will show you how to find the square root of 81275 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.

√81275 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 81275 to simplify the square root of 81275. 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 81275. The factors of 81275 are 1, 5, 25, 3251, 16255, and 81275. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 81275 divided by the greatest perfect square from the list of all factors of 81275. We determined above that the greatest perfect square from the list of all factors of 81275 is 25. Furthermore, 81275 divided by 25 is 3251, therefore B equals 3251.

Now we have A and B and can get our answer to 81275 in its simplest radical form as follows:

√81275 = A√B

√81275 = 5√3251

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 81275 to simplify the square root of 81275 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 81275 and then take the square root of that product. The prime factors that multiply together to make 81275 are 5 x 5 x 3251. When we strip out the pairs only, we get 5 x 5 = 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Divide 81275 by the number (A) squared. 5 squared is 25 and 81275 divided by 25 is 3251. Therefore, B equals 3251.

Once again we have A and B and can get our answer to 81275 in its simplest radical form as follows:

√81275 = A√B

√81275 = 5√3251

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Simplify Square Root of 81276
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