Simplify Square Root of 74375

Here we will show you two methods that you can use to simplify the square root of 74375. In other words, we will show you how to find the square root of 74375 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.

√74375 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 74375 to simplify the square root of 74375. 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 74375. The factors of 74375 are 1, 5, 7, 17, 25, 35, 85, 119, 125, 175, 425, 595, 625, 875, 2125, 2975, 4375, 10625, 14875, and 74375. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 74375 divided by the greatest perfect square from the list of all factors of 74375. We determined above that the greatest perfect square from the list of all factors of 74375 is 625. Furthermore, 74375 divided by 625 is 119, therefore B equals 119.

Now we have A and B and can get our answer to 74375 in its simplest radical form as follows:

√74375 = A√B

√74375 = 25√119

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 74375 to simplify the square root of 74375 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 74375 and then take the square root of that product. The prime factors that multiply together to make 74375 are 5 x 5 x 5 x 5 x 7 x 17. When we strip out the pairs only, we get 5 x 5 x 5 x 5 = 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Divide 74375 by the number (A) squared. 25 squared is 625 and 74375 divided by 625 is 119. Therefore, B equals 119.

Once again we have A and B and can get our answer to 74375 in its simplest radical form as follows:

√74375 = A√B

√74375 = 25√119

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Simplify Square Root of 74376
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