Simplify Square Root of 26558

Here we will show you two methods that you can use to simplify the square root of 26558. In other words, we will show you how to find the square root of 26558 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.

√26558 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26558 to simplify the square root of 26558. 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 26558. The factors of 26558 are 1, 2, 7, 14, 49, 98, 271, 542, 1897, 3794, 13279, and 26558. Furthermore, the greatest perfect square on this list is 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Calculate 26558 divided by the greatest perfect square from the list of all factors of 26558. We determined above that the greatest perfect square from the list of all factors of 26558 is 49. Furthermore, 26558 divided by 49 is 542, therefore B equals 542.

Now we have A and B and can get our answer to 26558 in its simplest radical form as follows:

√26558 = A√B

√26558 = 7√542

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26558 to simplify the square root of 26558 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 26558 and then take the square root of that product. The prime factors that multiply together to make 26558 are 2 x 7 x 7 x 271. When we strip out the pairs only, we get 7 x 7 = 49 and the square root of 49 is 7. Therefore, A equals 7.

B = Divide 26558 by the number (A) squared. 7 squared is 49 and 26558 divided by 49 is 542. Therefore, B equals 542.

Once again we have A and B and can get our answer to 26558 in its simplest radical form as follows:

√26558 = A√B

√26558 = 7√542

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Simplify Square Root of 26559
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