Simplify Square Root of 58378

Here we will show you two methods that you can use to simplify the square root of 58378. In other words, we will show you how to find the square root of 58378 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.

√58378 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 58378 to simplify the square root of 58378. 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 58378. The factors of 58378 are 1, 2, 17, 34, 101, 202, 289, 578, 1717, 3434, 29189, and 58378. Furthermore, the greatest perfect square on this list is 289 and the square root of 289 is 17. Therefore, A equals 17.

B = Calculate 58378 divided by the greatest perfect square from the list of all factors of 58378. We determined above that the greatest perfect square from the list of all factors of 58378 is 289. Furthermore, 58378 divided by 289 is 202, therefore B equals 202.

Now we have A and B and can get our answer to 58378 in its simplest radical form as follows:

√58378 = A√B

√58378 = 17√202

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 58378 to simplify the square root of 58378 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 58378 and then take the square root of that product. The prime factors that multiply together to make 58378 are 2 x 17 x 17 x 101. 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 58378 by the number (A) squared. 17 squared is 289 and 58378 divided by 289 is 202. Therefore, B equals 202.

Once again we have A and B and can get our answer to 58378 in its simplest radical form as follows:

√58378 = A√B

√58378 = 17√202

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Simplify Square Root of 58379
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