Simplify Square Root of 10175

Here we will show you two methods that you can use to simplify the square root of 10175. In other words, we will show you how to find the square root of 10175 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.

√10175 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10175 to simplify the square root of 10175. 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 10175. The factors of 10175 are 1, 5, 11, 25, 37, 55, 185, 275, 407, 925, 2035, and 10175. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 10175 divided by the greatest perfect square from the list of all factors of 10175. We determined above that the greatest perfect square from the list of all factors of 10175 is 25. Furthermore, 10175 divided by 25 is 407, therefore B equals 407.

Now we have A and B and can get our answer to 10175 in its simplest radical form as follows:

√10175 = A√B

√10175 = 5√407

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10175 to simplify the square root of 10175 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 10175 and then take the square root of that product. The prime factors that multiply together to make 10175 are 5 x 5 x 11 x 37. 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 10175 by the number (A) squared. 5 squared is 25 and 10175 divided by 25 is 407. Therefore, B equals 407.

Once again we have A and B and can get our answer to 10175 in its simplest radical form as follows:

√10175 = A√B

√10175 = 5√407

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Simplify Square Root of 10176
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