Simplify Square Root of 59000

Here we will show you two methods that you can use to simplify the square root of 59000. In other words, we will show you how to find the square root of 59000 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.

√59000 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 59000 to simplify the square root of 59000. 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 59000. The factors of 59000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 59, 100, 118, 125, 200, 236, 250, 295, 472, 500, 590, 1000, 1180, 1475, 2360, 2950, 5900, 7375, 11800, 14750, 29500, and 59000. Furthermore, the greatest perfect square on this list is 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Calculate 59000 divided by the greatest perfect square from the list of all factors of 59000. We determined above that the greatest perfect square from the list of all factors of 59000 is 100. Furthermore, 59000 divided by 100 is 590, therefore B equals 590.

Now we have A and B and can get our answer to 59000 in its simplest radical form as follows:

√59000 = A√B

√59000 = 10√590

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 59000 to simplify the square root of 59000 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 59000 and then take the square root of that product. The prime factors that multiply together to make 59000 are 2 x 2 x 2 x 5 x 5 x 5 x 59. When we strip out the pairs only, we get 2 x 2 x 5 x 5 = 100 and the square root of 100 is 10. Therefore, A equals 10.

B = Divide 59000 by the number (A) squared. 10 squared is 100 and 59000 divided by 100 is 590. Therefore, B equals 590.

Once again we have A and B and can get our answer to 59000 in its simplest radical form as follows:

√59000 = A√B

√59000 = 10√590

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Simplify Square Root of 59001
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