Simplify Square Root of 578

Here we will show you two methods that you can use to simplify the square root of 578. In other words, we will show you how to find the square root of 578 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.

√578 = A√B

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

B = Calculate 578 divided by the greatest perfect square from the list of all factors of 578. We determined above that the greatest perfect square from the list of all factors of 578 is 289. Furthermore, 578 divided by 289 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 578 in its simplest radical form as follows:

√578 = A√B

√578 = 17√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 578 to simplify the square root of 578 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 578 and then take the square root of that product. The prime factors that multiply together to make 578 are 2 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 578 by the number (A) squared. 17 squared is 289 and 578 divided by 289 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 578 in its simplest radical form as follows:

√578 = A√B

√578 = 17√2

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Simplify Square Root of 579
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