Simplify Square Root of 52598

Here we will show you two methods that you can use to simplify the square root of 52598. In other words, we will show you how to find the square root of 52598 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.

√52598 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 52598 to simplify the square root of 52598. 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 52598. The factors of 52598 are 1, 2, 7, 13, 14, 17, 26, 34, 91, 119, 182, 221, 238, 289, 442, 578, 1547, 2023, 3094, 3757, 4046, 7514, 26299, and 52598. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 52598 divided by the greatest perfect square from the list of all factors of 52598. We determined above that the greatest perfect square from the list of all factors of 52598 is 289. Furthermore, 52598 divided by 289 is 182, therefore B equals 182.

Now we have A and B and can get our answer to 52598 in its simplest radical form as follows:

√52598 = A√B

√52598 = 17√182

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 52598 to simplify the square root of 52598 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 52598 and then take the square root of that product. The prime factors that multiply together to make 52598 are 2 x 7 x 13 x 17 x 17. When we strip out the pairs only, we get 17 x 17 = 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Divide 52598 by the number (A) squared. 17 squared is 289 and 52598 divided by 289 is 182. Therefore, B equals 182.

Once again we have A and B and can get our answer to 52598 in its simplest radical form as follows:

√52598 = A√B

√52598 = 17√182

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Simplify Square Root of 52599
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