Simplify Square Root of 585

Here we will show you two methods that you can use to simplify the square root of 585. In other words, we will show you how to find the square root of 585 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.

√585 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 585 to simplify the square root of 585. 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 585. The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, and 585. Furthermore, the greatest perfect square on this list is 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Calculate 585 divided by the greatest perfect square from the list of all factors of 585. We determined above that the greatest perfect square from the list of all factors of 585 is 9. Furthermore, 585 divided by 9 is 65, therefore B equals 65.

Now we have A and B and can get our answer to 585 in its simplest radical form as follows:

√585 = A√B

√585 = 3√65

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 585 to simplify the square root of 585 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 585 and then take the square root of that product. The prime factors that multiply together to make 585 are 3 x 3 x 5 x 13. When we strip out the pairs only, we get 3 x 3 = 9 and the square root of 9 is 3. Therefore, A equals 3.

B = Divide 585 by the number (A) squared. 3 squared is 9 and 585 divided by 9 is 65. Therefore, B equals 65.

Once again we have A and B and can get our answer to 585 in its simplest radical form as follows:

√585 = A√B

√585 = 3√65

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Simplify Square Root of 586
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