Simplify Square Root of 63750

Here we will show you two methods that you can use to simplify the square root of 63750. In other words, we will show you how to find the square root of 63750 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.

√63750 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 63750 to simplify the square root of 63750. 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 63750. The factors of 63750 are 1, 2, 3, 5, 6, 10, 15, 17, 25, 30, 34, 50, 51, 75, 85, 102, 125, 150, 170, 250, 255, 375, 425, 510, 625, 750, 850, 1250, 1275, 1875, 2125, 2550, 3750, 4250, 6375, 10625, 12750, 21250, 31875, and 63750. Furthermore, the greatest perfect square on this list is 625 and the square root of 625 is 25. Therefore, A equals 25.

B = Calculate 63750 divided by the greatest perfect square from the list of all factors of 63750. We determined above that the greatest perfect square from the list of all factors of 63750 is 625. Furthermore, 63750 divided by 625 is 102, therefore B equals 102.

Now we have A and B and can get our answer to 63750 in its simplest radical form as follows:

√63750 = A√B

√63750 = 25√102

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 63750 to simplify the square root of 63750 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 63750 and then take the square root of that product. The prime factors that multiply together to make 63750 are 2 x 3 x 5 x 5 x 5 x 5 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 63750 by the number (A) squared. 25 squared is 625 and 63750 divided by 625 is 102. Therefore, B equals 102.

Once again we have A and B and can get our answer to 63750 in its simplest radical form as follows:

√63750 = A√B

√63750 = 25√102

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Simplify Square Root of 63751
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