Simplify Square Root of 78575

Here we will show you two methods that you can use to simplify the square root of 78575. In other words, we will show you how to find the square root of 78575 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.

√78575 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 78575 to simplify the square root of 78575. 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 78575. The factors of 78575 are 1, 5, 7, 25, 35, 175, 449, 2245, 3143, 11225, 15715, and 78575. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 78575 divided by the greatest perfect square from the list of all factors of 78575. We determined above that the greatest perfect square from the list of all factors of 78575 is 25. Furthermore, 78575 divided by 25 is 3143, therefore B equals 3143.

Now we have A and B and can get our answer to 78575 in its simplest radical form as follows:

√78575 = A√B

√78575 = 5√3143

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 78575 to simplify the square root of 78575 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 78575 and then take the square root of that product. The prime factors that multiply together to make 78575 are 5 x 5 x 7 x 449. 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 78575 by the number (A) squared. 5 squared is 25 and 78575 divided by 25 is 3143. Therefore, B equals 3143.

Once again we have A and B and can get our answer to 78575 in its simplest radical form as follows:

√78575 = A√B

√78575 = 5√3143

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Simplify Square Root of 78576
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