Simplify Square Root of 97865

Here we will show you two methods that you can use to simplify the square root of 97865. In other words, we will show you how to find the square root of 97865 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.

√97865 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 97865 to simplify the square root of 97865. 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 97865. The factors of 97865 are 1, 5, 23, 37, 115, 185, 529, 851, 2645, 4255, 19573, and 97865. Furthermore, the greatest perfect square on this list is 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Calculate 97865 divided by the greatest perfect square from the list of all factors of 97865. We determined above that the greatest perfect square from the list of all factors of 97865 is 529. Furthermore, 97865 divided by 529 is 185, therefore B equals 185.

Now we have A and B and can get our answer to 97865 in its simplest radical form as follows:

√97865 = A√B

√97865 = 23√185

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 97865 to simplify the square root of 97865 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 97865 and then take the square root of that product. The prime factors that multiply together to make 97865 are 5 x 23 x 23 x 37. When we strip out the pairs only, we get 23 x 23 = 529 and the square root of 529 is 23. Therefore, A equals 23.

B = Divide 97865 by the number (A) squared. 23 squared is 529 and 97865 divided by 529 is 185. Therefore, B equals 185.

Once again we have A and B and can get our answer to 97865 in its simplest radical form as follows:

√97865 = A√B

√97865 = 23√185

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Simplify Square Root of 97866
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