Simplify Square Root of 10375

Here we will show you two methods that you can use to simplify the square root of 10375. In other words, we will show you how to find the square root of 10375 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.

√10375 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10375 to simplify the square root of 10375. 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 10375. The factors of 10375 are 1, 5, 25, 83, 125, 415, 2075, and 10375. Furthermore, the greatest perfect square on this list is 25 and the square root of 25 is 5. Therefore, A equals 5.

B = Calculate 10375 divided by the greatest perfect square from the list of all factors of 10375. We determined above that the greatest perfect square from the list of all factors of 10375 is 25. Furthermore, 10375 divided by 25 is 415, therefore B equals 415.

Now we have A and B and can get our answer to 10375 in its simplest radical form as follows:

√10375 = A√B

√10375 = 5√415

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10375 to simplify the square root of 10375 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 10375 and then take the square root of that product. The prime factors that multiply together to make 10375 are 5 x 5 x 5 x 83. 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 10375 by the number (A) squared. 5 squared is 25 and 10375 divided by 25 is 415. Therefore, B equals 415.

Once again we have A and B and can get our answer to 10375 in its simplest radical form as follows:

√10375 = A√B

√10375 = 5√415

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Simplify Square Root of 10376
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