Simplify Square Root of 10580

Here we will show you two methods that you can use to simplify the square root of 10580. In other words, we will show you how to find the square root of 10580 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.

√10580 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 10580 to simplify the square root of 10580. 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 10580. The factors of 10580 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460, 529, 1058, 2116, 2645, 5290, and 10580. Furthermore, the greatest perfect square on this list is 2116 and the square root of 2116 is 46. Therefore, A equals 46.

B = Calculate 10580 divided by the greatest perfect square from the list of all factors of 10580. We determined above that the greatest perfect square from the list of all factors of 10580 is 2116. Furthermore, 10580 divided by 2116 is 5, therefore B equals 5.

Now we have A and B and can get our answer to 10580 in its simplest radical form as follows:

√10580 = A√B

√10580 = 46√5

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 10580 to simplify the square root of 10580 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 10580 and then take the square root of that product. The prime factors that multiply together to make 10580 are 2 x 2 x 5 x 23 x 23. When we strip out the pairs only, we get 2 x 2 x 23 x 23 = 2116 and the square root of 2116 is 46. Therefore, A equals 46.

B = Divide 10580 by the number (A) squared. 46 squared is 2116 and 10580 divided by 2116 is 5. Therefore, B equals 5.

Once again we have A and B and can get our answer to 10580 in its simplest radical form as follows:

√10580 = A√B

√10580 = 46√5

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Simplify Square Root of 10581
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