Simplify Square Root of 26702

Here we will show you two methods that you can use to simplify the square root of 26702. In other words, we will show you how to find the square root of 26702 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.

√26702 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26702 to simplify the square root of 26702. 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 26702. The factors of 26702 are 1, 2, 13, 26, 79, 158, 169, 338, 1027, 2054, 13351, and 26702. Furthermore, the greatest perfect square on this list is 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Calculate 26702 divided by the greatest perfect square from the list of all factors of 26702. We determined above that the greatest perfect square from the list of all factors of 26702 is 169. Furthermore, 26702 divided by 169 is 158, therefore B equals 158.

Now we have A and B and can get our answer to 26702 in its simplest radical form as follows:

√26702 = A√B

√26702 = 13√158

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26702 to simplify the square root of 26702 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 26702 and then take the square root of that product. The prime factors that multiply together to make 26702 are 2 x 13 x 13 x 79. When we strip out the pairs only, we get 13 x 13 = 169 and the square root of 169 is 13. Therefore, A equals 13.

B = Divide 26702 by the number (A) squared. 13 squared is 169 and 26702 divided by 169 is 158. Therefore, B equals 158.

Once again we have A and B and can get our answer to 26702 in its simplest radical form as follows:

√26702 = A√B

√26702 = 13√158

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Simplify Square Root of 26703
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