Simplify Square Root of 26406

Here we will show you two methods that you can use to simplify the square root of 26406. In other words, we will show you how to find the square root of 26406 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.

√26406 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 26406 to simplify the square root of 26406. 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 26406. The factors of 26406 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 163, 326, 489, 978, 1467, 2934, 4401, 8802, 13203, and 26406. Furthermore, the greatest perfect square on this list is 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Calculate 26406 divided by the greatest perfect square from the list of all factors of 26406. We determined above that the greatest perfect square from the list of all factors of 26406 is 81. Furthermore, 26406 divided by 81 is 326, therefore B equals 326.

Now we have A and B and can get our answer to 26406 in its simplest radical form as follows:

√26406 = A√B

√26406 = 9√326

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 26406 to simplify the square root of 26406 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 26406 and then take the square root of that product. The prime factors that multiply together to make 26406 are 2 x 3 x 3 x 3 x 3 x 163. When we strip out the pairs only, we get 3 x 3 x 3 x 3 = 81 and the square root of 81 is 9. Therefore, A equals 9.

B = Divide 26406 by the number (A) squared. 9 squared is 81 and 26406 divided by 81 is 326. Therefore, B equals 326.

Once again we have A and B and can get our answer to 26406 in its simplest radical form as follows:

√26406 = A√B

√26406 = 9√326

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Simplify Square Root of 26407
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