Simplify Square Root of 58621

Here we will show you two methods that you can use to simplify the square root of 58621. In other words, we will show you how to find the square root of 58621 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.

√58621 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58621 to simplify the square root of 58621. 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 58621. The factors of 58621 are 1, 31, 61, 961, 1891, and 58621. Furthermore, the greatest perfect square on this list is 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Calculate 58621 divided by the greatest perfect square from the list of all factors of 58621. We determined above that the greatest perfect square from the list of all factors of 58621 is 961. Furthermore, 58621 divided by 961 is 61, therefore B equals 61.

Now we have A and B and can get our answer to 58621 in its simplest radical form as follows:

√58621 = A√B

√58621 = 31√61

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58621 to simplify the square root of 58621 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 58621 and then take the square root of that product. The prime factors that multiply together to make 58621 are 31 x 31 x 61. When we strip out the pairs only, we get 31 x 31 = 961 and the square root of 961 is 31. Therefore, A equals 31.

B = Divide 58621 by the number (A) squared. 31 squared is 961 and 58621 divided by 961 is 61. Therefore, B equals 61.

Once again we have A and B and can get our answer to 58621 in its simplest radical form as follows:

√58621 = A√B

√58621 = 31√61

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Simplify Square Root of 58622
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