Simplify Square Root of 60750

Here we will show you two methods that you can use to simplify the square root of 60750. In other words, we will show you how to find the square root of 60750 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.

√60750 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 60750 to simplify the square root of 60750. 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 60750. The factors of 60750 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 81, 90, 125, 135, 150, 162, 225, 243, 250, 270, 375, 405, 450, 486, 675, 750, 810, 1125, 1215, 1350, 2025, 2250, 2430, 3375, 4050, 6075, 6750, 10125, 12150, 20250, 30375, and 60750. Furthermore, the greatest perfect square on this list is 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Calculate 60750 divided by the greatest perfect square from the list of all factors of 60750. We determined above that the greatest perfect square from the list of all factors of 60750 is 2025. Furthermore, 60750 divided by 2025 is 30, therefore B equals 30.

Now we have A and B and can get our answer to 60750 in its simplest radical form as follows:

√60750 = A√B

√60750 = 45√30

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 60750 to simplify the square root of 60750 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 60750 and then take the square root of that product. The prime factors that multiply together to make 60750 are 2 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5. When we strip out the pairs only, we get 3 x 3 x 3 x 3 x 5 x 5 = 2025 and the square root of 2025 is 45. Therefore, A equals 45.

B = Divide 60750 by the number (A) squared. 45 squared is 2025 and 60750 divided by 2025 is 30. Therefore, B equals 30.

Once again we have A and B and can get our answer to 60750 in its simplest radical form as follows:

√60750 = A√B

√60750 = 45√30

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