Simplify Square Root of 26588

Here we will show you two methods that you can use to simplify the square root of 26588. In other words, we will show you how to find the square root of 26588 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.

√26588 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26588 to simplify the square root of 26588. 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 26588. The factors of 26588 are 1, 2, 4, 17, 23, 34, 46, 68, 92, 289, 391, 578, 782, 1156, 1564, 6647, 13294, and 26588. Furthermore, the greatest perfect square on this list is 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Calculate 26588 divided by the greatest perfect square from the list of all factors of 26588. We determined above that the greatest perfect square from the list of all factors of 26588 is 1156. Furthermore, 26588 divided by 1156 is 23, therefore B equals 23.

Now we have A and B and can get our answer to 26588 in its simplest radical form as follows:

√26588 = A√B

√26588 = 34√23

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26588 to simplify the square root of 26588 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 26588 and then take the square root of that product. The prime factors that multiply together to make 26588 are 2 x 2 x 17 x 17 x 23. When we strip out the pairs only, we get 2 x 2 x 17 x 17 = 1156 and the square root of 1156 is 34. Therefore, A equals 34.

B = Divide 26588 by the number (A) squared. 34 squared is 1156 and 26588 divided by 1156 is 23. Therefore, B equals 23.

Once again we have A and B and can get our answer to 26588 in its simplest radical form as follows:

√26588 = A√B

√26588 = 34√23

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Simplify Square Root of 26589
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